From 08198be8daeb316854a72dfcf7b52f73430a4560 Mon Sep 17 00:00:00 2001
From: achekery <6503526+achekery@users.noreply.github.com>
Date: Tue, 12 May 2026 15:25:51 -0700
Subject: [PATCH 01/12] add skeleton versions

---
 .github/workflows/docs.yml          |  18 +
 DEVELOPMENT.md                      |   3 +
 docs/development.md                 |  43 +++
 docs/dynamic_interval_management.md |  82 +++++
 docs/dynamic_point_aggregation.md   |  85 +++++
 docs/index.md                       |   5 +
 docs/suffix_pattern_recognition.md  |  30 ++
 mkdocs.yml                          |  35 ++
 pyproject.toml                      |   5 +
 uv.lock                             | 553 ++++++++++++++++++++++++++++
 10 files changed, 859 insertions(+)
 create mode 100644 .github/workflows/docs.yml
 create mode 100644 docs/development.md
 create mode 100644 docs/dynamic_interval_management.md
 create mode 100644 docs/dynamic_point_aggregation.md
 create mode 100644 docs/index.md
 create mode 100644 docs/suffix_pattern_recognition.md
 create mode 100644 mkdocs.yml

diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml
new file mode 100644
index 0000000..52eeb2d
--- /dev/null
+++ b/.github/workflows/docs.yml
@@ -0,0 +1,18 @@
+name: docs
+on:
+  push:
+    branches: [main]
+
+jobs:
+  deploy:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - name: Install uv
+        uses: astral-sh/setup-uv@v3
+      - name: Setup Python
+        run: uv python install 3.13
+      - name: Build and Deploy
+        run: |
+          uv sync --group docs
+          uv run mkdocs gh-deploy --force
diff --git a/DEVELOPMENT.md b/DEVELOPMENT.md
index 0142f9a..ddf30cf 100644
--- a/DEVELOPMENT.md
+++ b/DEVELOPMENT.md
@@ -37,4 +37,7 @@ uv run --group dev --extra benchmark pytest -sv
 
 # Watch run until it completes.
 gh run watch
+
+# Show project files.
+(git ls-files | xargs tail -n +1) 2>&1 >var/files.txt
 ```
diff --git a/docs/development.md b/docs/development.md
new file mode 100644
index 0000000..ddf30cf
--- /dev/null
+++ b/docs/development.md
@@ -0,0 +1,43 @@
+
+data_streaming_accelerators/
+├── .github/workflows/
+├── docs/
+│   └── mkdocs.yml
+├── src/
+│   └── data_streaming_accelerators/
+│       ├── __init__.py
+│       ├── __main__.py
+│       ├── core/
+│       |   ├── dynamic_interval_management.py
+│       |   ├── dynamic_point_aggregation.py
+│       |   └── suffix_pattern_recognition.py
+│       ├── api.py
+├── tests/
+│   ├── conftest.py
+│   ├── test_api.py
+│   ├── test_core.py
+├── .gitignore
+├── pyproject.toml
+├── README.md
+└── LICENSE
+
+```sh
+# https://docs.astral.sh/uv/getting-started/installation/
+# install uv from official installer
+wget -qO- https://astral.sh/uv/install.sh | sh
+```
+
+```
+# Run specific markers in pytest
+uv run --group dev --extra benchmark pytest -sv -m func
+uv run --group dev --extra benchmark pytest -sv -m perf
+
+# Run pytest
+uv run --group dev --extra benchmark pytest -sv
+
+# Watch run until it completes.
+gh run watch
+
+# Show project files.
+(git ls-files | xargs tail -n +1) 2>&1 >var/files.txt
+```
diff --git a/docs/dynamic_interval_management.md b/docs/dynamic_interval_management.md
new file mode 100644
index 0000000..227f6da
--- /dev/null
+++ b/docs/dynamic_interval_management.md
@@ -0,0 +1,82 @@
+# Data Streaming Accelerators
+
+![Python CI](https://github.com/achekery/data-streaming/actions/workflows/python-app.yml/badge.svg)
+
+## Dynamic Interval Management
+
+### 1. Design Summary
+The theoretical lower bound for merging $N$ static intervals is $\Omega(N \log N)$ due to the sorting requirement. By focusing on interval edges rather than the source intervals themselves, we can focus on efficient algorithms with compact implementation.  However, in **Online Streaming Environments**, the task shifts from batch data loading (static intervals) to streaming data ingestion (dynamic intervals).
+
+#### 📊 Complexity Analysis
+
+| Operation | Batch Variants (v1/v2) | Streaming Variant (v3) | Comparison |
+| :--- | :--- | :--- | :--- |
+| **Initial Setup** | $O(N \log N)$ | $O(N \log N)$ | Equivalent |
+| **Batch Updates (N)** | $O(N \log N)$ | $O(N \log N)$ | Equivalent |
+| **Streaming Updates (1)** | $O(N \log N)$ | **$O(\log N)$** | **Streaming Variant** is superior |
+| **Space Complexity** | $O(N)$ | $O(N)$ | Equivalent |
+
+#### 🚀 The Pruning Logic (Visual)
+
+The advantage of an Augmented AVL Interval Tree is its ability to prune search branches that cannot contain an overlap, ensuring $O(\log N)$ search time.
+
+![Diagram of Pruning Logic](dynamic_interval_management/static/pruning-diagram.png)
+
+### 2. Design Approaches
+
+### Optimal Approaches for Batch Data (Static Intervals)
+* **Sweep-line (Variant 1):** Uses a sorted list of edge objects and a counter.
+    * **Complexity (Batch):** $O(N \log N)$ setup, $O(N)$ calculation. 
+    * **Complexity (Streaming):** $O(N \log N)$ per `insert`/`put` operation.
+    * **Verdict:** Suitable for batch case due to second-best ~16ms benchmark with static intervals impacted by object-overhead during calculation. Not suitable for streaming case due to high complexity.
+* **Two-Pointer Search (Variant 2):** Uses two sorted edge arrays and two pointers.
+    * **Complexity (Batch):** $O(N \log N)$ setup, $O(N)$ calculation.
+    * **Complexity (Streaming):** $O(N \log N)$ per `insert`/`put` operation.
+    * **Verdict:** Suitable for batch case due to best-in-class ~7ms benchmark with static intervals. Not suitable for streaming case due to high complexity.
+
+### Optimal Approaches for Streaming Data (Dynamic Intervals)
+* **Augmented AVL Interval Tree (Variant 3):** A stateful, self-balancing BST.
+    * **Complexity (Batch):** $O(N \log N)$ setup, $O(N)$ calculation. 
+    * **Complexity (Streaming):** $O(\log N)$ per `insert`/`put` operation.
+    * **Verdict:** Not suitable for batch case due to poor ~4130ms benchmark with static intervals impacted by object-overhead during calculation. Suitable for streaming case due to best-in-class complexity per `insert`/`put` operation. Notice the optimal approaches for batch data merging are easier to maintain, with **90% fewer LOC** (~25 vs ~250)! 
+
+### 3. Design Trade-offs
+
+#### The Efficiency Paradox
+In benchmarks with static intervals, the Two-Pointer Search (Variant 2) was **400x faster** than the Interval Tree (Variant 3). However, in **Online Streaming Environments**, the Two-Pointer Search overall complexity degrades to $O(N^2 \log N)$ over a series of $N$ updates while the Interval Tree overall complexity maintains $O(N \log N)$.
+
+#### Streaming Benchmark Results
+In benchmarks with dynamic intervals up to $N=3000$, the Interval Tree (Variant 3) was as much as **50x faster** than the Two-Pointer Search (Variant 2).  While the Two-Pointer Search (Variant 2) is faster for a single batch run, it fails to scale in an **Online Streaming Environment** where the merged state must be updated for every new interval. As $N$ increases, the Two-Pointer Search runtime explodes quadratically while the Interval Tree runtime continues linearly.
+
+| Input Size (N) | Batch-Style (s) | Tree-Style (s) | Speedup |
+| :--- | :--- | :--- | :--- |
+| 100 | 0.0015 | 0.0021 | 0.7x |
+| 500 | 0.0359 | 0.0140 | 2.6x |
+| 1000 | 0.1501 | 0.0230 | 6.5x |
+| 2000 | 0.6743 | 0.0383 | 17.6x |
+| 3000 | 1.6093 | 0.0318 | **50.6x** |
+
+![Graph for Performance Report](dynamic_interval_management/static/performance-report-1280x640.png)
+
+### 4. Design Optimizations
+
+#### Augmented Metadata
+By augmenting the BST with `subtree_max` metadata, I reduced the search-and-merge task from a linear scan to a logarithmic search. This allows the streaming platform to maintain a "Live" merged state with $O(\log N)$ latency per request.
+
+#### Invariant-Driven Correctness
+To ensure system reliability during high-frequency updates, I prioritized **Correctness by Design** by explicitly maintaining the AVL balance and metadata invariants during every mutation (`insert`, `delete`).
+
+#### Architectural Hardening
+By implementing a **Sentinel Node Architecture** with a **Two-Down** AVL balancing subtree rotation strategy and removing the need for sentinel node checks throughout the codebase, I simplified the balancing feature and provided a cleaner and more maintainable implementation.
+
+#### Python Object-Model Tuning
+To reduce object-overhead due to the Python object-model, I implemented **Attribute Flattening**. After replacing packed collections (`self.interval[0]`) with discrete integers (`self.lo`, `self.hi`), I reduced constant factors in the hot execution path and achieved a **15% reduction** in benchmarks with static intervals.
+
+### 5. Getting Started
+
+This design requires **Python 3.13+**.
+
+To run the regression tests for this design:
+```bash
+uv run --group dev --extra benchmark pytest -sv
+```
diff --git a/docs/dynamic_point_aggregation.md b/docs/dynamic_point_aggregation.md
new file mode 100644
index 0000000..9e3ebc1
--- /dev/null
+++ b/docs/dynamic_point_aggregation.md
@@ -0,0 +1,85 @@
+# Dynamic Point Aggregation
+![Python CI](https://github.com/achekery/data-streaming/actions/workflows/python-app.yml/badge.svg)
+
+## 1. Design Summary
+The optimal runtime complexity for dynamic point aggregation from $N$ point values to $O(N)$ disjoint intervals is $\Omega(N \log N)$ due to the ordering requirement. The request handler uses `put` requests to add new values and `get` requests to make a new interval sequence.
+
+Because offline scenarios (batch data) have known usage patterns, the batch variant (V1) can **optimize the hot path** by simplifying high-usage `put` requests to $O(1)$ and expanding low-usage `get` requests to $O(N \log N)$.
+
+However, because online scenarios (streaming data) do not have known usage patterns, the streaming variant (V2) must instead **balance complexity** between `put` requests ($O(\log N)$) and `get` requests ($O(N)$).
+
+### 📊 Complexity Analysis
+
+| Operation | Batch Variant (V1) | Streaming Variant (V2) | Comparison |
+| :--- | :--- | :--- | :--- |
+| **Initial Setup** | $O(1)$ | $O(1)$ | Equivalent |
+| **Batch Updates (N Put, 1 Get)** | $O(N \log N)$ | $O(N \log N)$ | Equivalent |
+| **Streaming Updates (N Put, K Get)** | $O(K*N \log N)$ | $O(N \log N + K * N)$ | **V2 is Superior** |
+| **Space Complexity** | $O(N)$ | $O(N)$ | Equivalent
+
+## 2. Design Details
+The batch variant (V1) uses an unordered set to add new values as data points in $O(1)$ per `put` request and does one pass over a new sorted list with sweep line method to generate disjoint intervals in $O(N \log N)$ per `get` request.
+
+The streaming variant (V2) uses two sorted sets with binary search to add new values as interval bounds in $O(\log N)$ per `put` request (or $O(\sqrt N)$ with python `sortedcontainers`) and does one pass over the existing sorted sets with sweep line method to generate disjoint intervals in $O(N)$ per `get` request.
+
+## 3. Design Trade-offs
+
+### The Efficiency Paradox
+Although the batch variant (V1) was **2.7x faster** in small-scale offline scenarios (N=100, R=0.1), the streaming variant (V2) was **6.4x faster** in large-scale online scenarios (N=50000, R=0.5). This performance gain in online scenarios was due to the runtime complexity of the streaming variant at $O(N \log N + K*N)$ increasing more slowly with data size compared to the batch variant at $O(K*N \log N)$.
+
+With python `sortedcontainers`, these runtime complexities were instead $O(N \sqrt N + K*N)$ and $O(K*N \log N)$ respectively. Although the streaming variant was still faster, the performance gain was less dramatic since $O(\sqrt N)$ increases faster than $O(\log N)$.
+
+### Streaming Benchmark Results
+When the request traffic was mostly `put` requests (R=0.1) to simulate offline scenarios, the batch variant (V1) was 2.7x faster when data size was smaller (N=100) and the streaming variant was **4.9x faster** when data size was larger (N=50000).
+
+![Speedup by Data Size (R=0.1)](dynamic_point_aggregation/static/speedup_by_data_size_request_distr0.1.png)
+
+When the request traffic was balanced beween `put` and `get` requests (R=0.5) to simulate online scenarios, the batch variant (V1) was **1.2x faster** when data size was smaller (N=100) and the streaming variant was **6.4x faster** when data size was larger (N=50000).
+
+![Speedup by Data Size (R=0.5)](dynamic_point_aggregation/static/speedup_by_data_size_request_distr0.5.png)
+
+These results highlight that the batch variant (V1) is suitable for smaller data streams and offline scenarios, whereas the streaming variant (V2) is suitable for larger data streams and online scenarios.
+
+| TestCaseID | DataSize | RequestDistribution | V1TimeElapsed | V2TimeElapsed | SpeedupV1V2 | SpeedupV2V1 |
+| :--- | :--- | :--- | :--- | :--- | :--- | :--- |
+| 0 | 100 | 0.100 | 0.000 | 0.001 | 2.706 | 0.370 |
+| 1 | 100 | 0.200 | 0.000 | 0.001 | 1.998 | 0.500 |
+| 2 | 100 | 0.500 | 0.001 | 0.001 | 1.289 | 0.776 |
+| 3 | 100 | 0.800 | 0.002 | 0.003 | 1.042 | 0.960 |
+| 4 | 200 | 0.100 | 0.001 | 0.001 | 2.115 | 0.473 |
+| 5 | 200 | 0.200 | 0.001 | 0.001 | 1.642 | 0.609 |
+| 6 | 200 | 0.500 | 0.003 | 0.003 | 1.010 | 0.990 |
+| 7 | 200 | 0.800 | 0.013 | 0.010 | 0.821 | 1.218 |
+| 8 | 500 | 0.100 | 0.002 | 0.003 | 1.606 | 0.623 |
+| 9 | 500 | 0.200 | 0.004 | 0.005 | 1.116 | 0.896 |
+| 10 | 500 | 0.500 | 0.020 | 0.016 | 0.816 | 1.226 |
+| 11 | 500 | 0.800 | 0.071 | 0.051 | 0.726 | 1.378 |
+| 12 | 1000 | 0.100 | 0.008 | 0.009 | 1.059 | 0.944 |
+| 13 | 1000 | 0.200 | 0.016 | 0.014 | 0.861 | 1.162 |
+| 14 | 1000 | 0.500 | 0.070 | 0.050 | 0.715 | 1.400 |
+| 15 | 1000 | 0.800 | 0.273 | 0.186 | 0.680 | 1.471 |
+| 16 | 2000 | 0.100 | 0.028 | 0.025 | 0.920 | 1.087 |
+| 17 | 2000 | 0.200 | 0.059 | 0.046 | 0.776 | 1.289 |
+| 18 | 2000 | 0.500 | 0.236 | 0.159 | 0.671 | 1.489 |
+| 19 | 2000 | 0.800 | 1.002 | 0.651 | 0.650 | 1.538 |
+| 20 | 5000 | 0.100 | 0.140 | 0.105 | 0.751 | 1.331 |
+| 21 | 5000 | 0.200 | 0.326 | 0.216 | 0.663 | 1.509 |
+| 22 | 5000 | 0.500 | 1.251 | 0.735 | 0.587 | 1.703 |
+| 23 | 5000 | 0.800 | 5.099 | 3.020 | 0.592 | 1.688 |
+| 24 | 10000 | 0.100 | 0.466 | 0.266 | 0.572 | 1.748 |
+| 25 | 10000 | 0.200 | 1.031 | 0.541 | 0.525 | 1.906 |
+| 26 | 10000 | 0.500 | 4.038 | 1.950 | 0.483 | 2.071 |
+| 27 | 10000 | 0.800 | 15.824 | 7.414 | 0.469 | 2.134 |
+| 28 | 20000 | 0.100 | 1.198 | 0.504 | 0.421 | 2.376 |
+| 29 | 20000 | 0.200 | 2.633 | 0.990 | 0.376 | 2.660 |
+| 30 | 20000 | 0.500 | 10.557 | 3.617 | 0.343 | 2.919 |
+| 31 | 20000 | 0.800 | 42.168 | 14.237 | 0.338 | 2.962 |
+| 32 | 50000 | 0.100 | 3.473 | 0.695 | 0.200 | 4.996 |
+| 33 | 50000 | 0.200 | 7.765 | 1.349 | 0.174 | 5.757 |
+| 34 | 50000 | 0.500 | 30.483 | 4.756 | 0.156 | 6.410 |
+| 35 | 50000 | 0.800 | 122.369 | 19.013 | 0.155 | 6.436 |
+
+## 4. Design Optimizations
+
+### State Transitions
+To ensure new point values are correctly merged with existing disjoint intervals, I applied **Correctness by Design** by separately handling the 3 overlap cases: the enclosed-by case (early exit if lower and upper bounds at insertion point are already aligned), the adjacent-to case (join with 1 or 2 neighbors if lower and upper bounds at insertion point are adjacent), and the distinct-from case (insert as new lower and upper bounds).
diff --git a/docs/index.md b/docs/index.md
new file mode 100644
index 0000000..5e733fd
--- /dev/null
+++ b/docs/index.md
@@ -0,0 +1,5 @@
+# Data Streaming Accelerators
+
+![Python CI](https://github.com/achekery/data-streaming/actions/workflows/python-app.yml/badge.svg)
+
+TODO: Add a high-level summary of the whole suite
diff --git a/docs/suffix_pattern_recognition.md b/docs/suffix_pattern_recognition.md
new file mode 100644
index 0000000..2ae450c
--- /dev/null
+++ b/docs/suffix_pattern_recognition.md
@@ -0,0 +1,30 @@
+# Suffix Pattern Recognition
+![Python CI](https://github.com/achekery/data-streaming/actions/workflows/python-app.yml/badge.svg)
+
+## 1. Design Summary
+For suffix pattern recognition with $K$ suffix patterns (length $W$) and 1 query pattern (length $N$), using **reverse-traversal prefix tree search** is efficient because it can model common ancestor ordering with reverse encoding (by inserting suffix patterns in reverse order during setup and searching in reverse order during queries) and check the multiple patterns over a single root-to-leaf pass (taking runtime $O(K\*W)$ for one-time setup and $O(W)$ for each query). This improves over using direct suffix pattern search which must check the multiple patterns over separate array passes (taking $O(K\*W)$ for each query) or using forward-traversal prefix tree search which cannot model common ancestor ordering and must check the multiple patterns over separate root-to-leaf passes (taking runtime $O(K\*W)$ for one-time setup and $O(K\*W)$ for each query).
+
+For batch data (offline scenario), reading the query pattern from a static array (size $N$) with a reverse iterator takes $O(1)$ auxiliary space. For streaming data (online scenario), reading the query pattern from a history array (size $W$) reconstructed from the stream takes $O(W)$ auxiliary space.
+
+### 📊 Complexity Analysis
+
+| Operation | Direct Search (v1) | Forward-traversal (v2) | Reverse-traversal (v3) | Comparison |
+| :--- | :--- | :--- | :--- | :--- |
+| **Initial Setup** | $O(1)$ | $O(K\*W)$ | $O(K\*W)$ | v1 is superior |
+| **Batch Queries (N)** | $O(K\*W)$ | $O(K\*W)$ | $O(W)$ | v3 is superior |
+| **Streaming Queries (1)** | $O(K\*W)$ | $O(K\*W)$ | $O(W)$ | v3 is superior |
+| **Space Complexity** | $O(1)$ | $O(K\*W)$ | $O(K\*W)$ | v1 is superior |
+
+### 🚀 Reverse Encoding (Visual)
+
+The advantage of reverse-traversal prefix tree search is that it can check multiple suffix patterns at once, ensuring $O(W)$ query time (and is independent of the suffix pattern count $K$ and the query pattern length $N$). This is possible because of reverse encoding.
+
+![Diagram for reverse encoding](suffix_pattern_recognition/static/diagram-image.png)
+
+## 2. Design Approaches & Trade-offs
+
+### When Less is More
+Although Direct Search (v1) requires ~90% less lines of code, it performs worse than Reverse-traversal (v3) in every comparison other than initial setup and space complexity. This trade-off shows that Direct Search may be preferable for low-memory systems that cannot afford higher space usage (like embedded systems) or greater maintenance scope (like regulated industries) and that Reverse-traversal may be preferable for systems with more resources (like compute nodes in distributed systems).
+
+### Python Object-Model Tuning
+To reduce object-overhead due to the Python object-model, I implemented a **nested hash map** for the reverse-traversal prefix tree, with each "node" using a character for the hash map key and a reference to the next "node" for the hash map value. This approach reduced object lookup during queries.
diff --git a/mkdocs.yml b/mkdocs.yml
new file mode 100644
index 0000000..644ded1
--- /dev/null
+++ b/mkdocs.yml
@@ -0,0 +1,35 @@
+site_name: Data Streaming Accelerators
+theme:
+  name: material
+  features:
+    - content.code.copy
+    - content.code.annotate
+    - navigation.sections
+
+markdown_extensions:
+  - pymdownx.superfences:
+      custom_fences:
+        - name: mermaid
+          class: mermaid
+          format: !!python/name:pymdownx.superfences.fence_code_format
+  - pymdownx.arithmatex:
+      generic: true # For your O(log N) LaTeX notations
+
+plugins:
+  - search
+  - mkdocstrings:
+      handlers:
+        python:
+          paths: [src]
+          options:
+            show_source: true
+            show_root_heading: true
+            show_category_heading: true
+
+nav:
+  - Overview: index.md
+  - Modules:
+    - Dynamic Interval Management: dynamic_interval_management.md
+    - Dynamic Point Aggregation: dynamic_point_aggregation.md
+    - Suffix Pattern Recognition: suffix_pattern_recognition.md
+  - Development: development.md
diff --git a/pyproject.toml b/pyproject.toml
index 5901882..2157f86 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -16,6 +16,11 @@ benchmark = [
 dev = [
     "pytest>=9.0.3",
 ]
+docs = [
+    "mkdocs-material>=9.7.6",
+    "mkdocs-mermaid2-plugin>=1.2.3",
+    "mkdocstrings[python]>=1.0.4",
+]
 lint = [
     "ruff>=0.15.12",
 ]
diff --git a/uv.lock b/uv.lock
index a9141dd..62730d8 100644
--- a/uv.lock
+++ b/uv.lock
@@ -10,6 +10,119 @@ resolution-markers = [
     "python_full_version < '3.14' and sys_platform != 'emscripten' and sys_platform != 'win32'",
 ]
 
+[[package]]
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+version = "2.18.0"
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+]
+
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+name = "backrefs"
+version = "7.0"
+source = { registry = "https://pypi.org/simple" }
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From da95a3b0ef99cb4900c8314f4f4f5f34f3c273c1 Mon Sep 17 00:00:00 2001
From: achekery <6503526+achekery@users.noreply.github.com>
Date: Tue, 12 May 2026 15:30:01 -0700
Subject: [PATCH 02/12] add api reference

---
 docs/dynamic_interval_management.md | 39 +++++++++++++++--------------
 docs/dynamic_point_aggregation.md   |  4 +++
 docs/suffix_pattern_recognition.md  |  4 +++
 3 files changed, 28 insertions(+), 19 deletions(-)

diff --git a/docs/dynamic_interval_management.md b/docs/dynamic_interval_management.md
index 227f6da..325d0a3 100644
--- a/docs/dynamic_interval_management.md
+++ b/docs/dynamic_interval_management.md
@@ -1,13 +1,10 @@
-# Data Streaming Accelerators
-
+# Dynamic Interval Management
 ![Python CI](https://github.com/achekery/data-streaming/actions/workflows/python-app.yml/badge.svg)
 
-## Dynamic Interval Management
-
-### 1. Design Summary
+## 1. Design Summary
 The theoretical lower bound for merging $N$ static intervals is $\Omega(N \log N)$ due to the sorting requirement. By focusing on interval edges rather than the source intervals themselves, we can focus on efficient algorithms with compact implementation.  However, in **Online Streaming Environments**, the task shifts from batch data loading (static intervals) to streaming data ingestion (dynamic intervals).
 
-#### 📊 Complexity Analysis
+### 📊 Complexity Analysis
 
 | Operation | Batch Variants (v1/v2) | Streaming Variant (v3) | Comparison |
 | :--- | :--- | :--- | :--- |
@@ -16,15 +13,15 @@ The theoretical lower bound for merging $N$ static intervals is $\Omega(N \log N
 | **Streaming Updates (1)** | $O(N \log N)$ | **$O(\log N)$** | **Streaming Variant** is superior |
 | **Space Complexity** | $O(N)$ | $O(N)$ | Equivalent |
 
-#### 🚀 The Pruning Logic (Visual)
+### 🚀 The Pruning Logic (Visual)
 
 The advantage of an Augmented AVL Interval Tree is its ability to prune search branches that cannot contain an overlap, ensuring $O(\log N)$ search time.
 
 ![Diagram of Pruning Logic](dynamic_interval_management/static/pruning-diagram.png)
 
-### 2. Design Approaches
+## 2. Design Approaches
 
-### Optimal Approaches for Batch Data (Static Intervals)
+## Optimal Approaches for Batch Data (Static Intervals)
 * **Sweep-line (Variant 1):** Uses a sorted list of edge objects and a counter.
     * **Complexity (Batch):** $O(N \log N)$ setup, $O(N)$ calculation. 
     * **Complexity (Streaming):** $O(N \log N)$ per `insert`/`put` operation.
@@ -34,18 +31,18 @@ The advantage of an Augmented AVL Interval Tree is its ability to prune search b
     * **Complexity (Streaming):** $O(N \log N)$ per `insert`/`put` operation.
     * **Verdict:** Suitable for batch case due to best-in-class ~7ms benchmark with static intervals. Not suitable for streaming case due to high complexity.
 
-### Optimal Approaches for Streaming Data (Dynamic Intervals)
+## Optimal Approaches for Streaming Data (Dynamic Intervals)
 * **Augmented AVL Interval Tree (Variant 3):** A stateful, self-balancing BST.
     * **Complexity (Batch):** $O(N \log N)$ setup, $O(N)$ calculation. 
     * **Complexity (Streaming):** $O(\log N)$ per `insert`/`put` operation.
     * **Verdict:** Not suitable for batch case due to poor ~4130ms benchmark with static intervals impacted by object-overhead during calculation. Suitable for streaming case due to best-in-class complexity per `insert`/`put` operation. Notice the optimal approaches for batch data merging are easier to maintain, with **90% fewer LOC** (~25 vs ~250)! 
 
-### 3. Design Trade-offs
+## 3. Design Trade-offs
 
-#### The Efficiency Paradox
+### The Efficiency Paradox
 In benchmarks with static intervals, the Two-Pointer Search (Variant 2) was **400x faster** than the Interval Tree (Variant 3). However, in **Online Streaming Environments**, the Two-Pointer Search overall complexity degrades to $O(N^2 \log N)$ over a series of $N$ updates while the Interval Tree overall complexity maintains $O(N \log N)$.
 
-#### Streaming Benchmark Results
+### Streaming Benchmark Results
 In benchmarks with dynamic intervals up to $N=3000$, the Interval Tree (Variant 3) was as much as **50x faster** than the Two-Pointer Search (Variant 2).  While the Two-Pointer Search (Variant 2) is faster for a single batch run, it fails to scale in an **Online Streaming Environment** where the merged state must be updated for every new interval. As $N$ increases, the Two-Pointer Search runtime explodes quadratically while the Interval Tree runtime continues linearly.
 
 | Input Size (N) | Batch-Style (s) | Tree-Style (s) | Speedup |
@@ -58,21 +55,21 @@ In benchmarks with dynamic intervals up to $N=3000$, the Interval Tree (Variant
 
 ![Graph for Performance Report](dynamic_interval_management/static/performance-report-1280x640.png)
 
-### 4. Design Optimizations
+## 4. Design Optimizations
 
-#### Augmented Metadata
+### Augmented Metadata
 By augmenting the BST with `subtree_max` metadata, I reduced the search-and-merge task from a linear scan to a logarithmic search. This allows the streaming platform to maintain a "Live" merged state with $O(\log N)$ latency per request.
 
-#### Invariant-Driven Correctness
+### Invariant-Driven Correctness
 To ensure system reliability during high-frequency updates, I prioritized **Correctness by Design** by explicitly maintaining the AVL balance and metadata invariants during every mutation (`insert`, `delete`).
 
-#### Architectural Hardening
+### Architectural Hardening
 By implementing a **Sentinel Node Architecture** with a **Two-Down** AVL balancing subtree rotation strategy and removing the need for sentinel node checks throughout the codebase, I simplified the balancing feature and provided a cleaner and more maintainable implementation.
 
-#### Python Object-Model Tuning
+### Python Object-Model Tuning
 To reduce object-overhead due to the Python object-model, I implemented **Attribute Flattening**. After replacing packed collections (`self.interval[0]`) with discrete integers (`self.lo`, `self.hi`), I reduced constant factors in the hot execution path and achieved a **15% reduction** in benchmarks with static intervals.
 
-### 5. Getting Started
+## 5. Getting Started
 
 This design requires **Python 3.13+**.
 
@@ -80,3 +77,7 @@ To run the regression tests for this design:
 ```bash
 uv run --group dev --extra benchmark pytest -sv
 ```
+
+## 6. API Reference
+
+::: data_streaming_accelerators.core.dynamic_interval_management.DynamicIntervalManagementV3
diff --git a/docs/dynamic_point_aggregation.md b/docs/dynamic_point_aggregation.md
index 9e3ebc1..c26e267 100644
--- a/docs/dynamic_point_aggregation.md
+++ b/docs/dynamic_point_aggregation.md
@@ -83,3 +83,7 @@ These results highlight that the batch variant (V1) is suitable for smaller data
 
 ### State Transitions
 To ensure new point values are correctly merged with existing disjoint intervals, I applied **Correctness by Design** by separately handling the 3 overlap cases: the enclosed-by case (early exit if lower and upper bounds at insertion point are already aligned), the adjacent-to case (join with 1 or 2 neighbors if lower and upper bounds at insertion point are adjacent), and the distinct-from case (insert as new lower and upper bounds).
+
+## 5. API Reference
+
+::: data_streaming_accelerators.core.dynamic_point_aggregation.DynamicPointAggregationV2
diff --git a/docs/suffix_pattern_recognition.md b/docs/suffix_pattern_recognition.md
index 2ae450c..72c5289 100644
--- a/docs/suffix_pattern_recognition.md
+++ b/docs/suffix_pattern_recognition.md
@@ -28,3 +28,7 @@ Although Direct Search (v1) requires ~90% less lines of code, it performs worse
 
 ### Python Object-Model Tuning
 To reduce object-overhead due to the Python object-model, I implemented a **nested hash map** for the reverse-traversal prefix tree, with each "node" using a character for the hash map key and a reference to the next "node" for the hash map value. This approach reduced object lookup during queries.
+
+## 3. API Reference
+
+::: data_streaming_accelerators.core.suffix_pattern_recognition.SuffixPatternRecognitionV1

From 4a8958e6a127649fcedd40490385a7a82e54a386 Mon Sep 17 00:00:00 2001
From: achekery <6503526+achekery@users.noreply.github.com>
Date: Tue, 12 May 2026 18:17:44 -0700
Subject: [PATCH 03/12] add markdown files in docs/modules

---
 docs/development.md                           | 43 -------------------
 docs/dynamic_interval_management/README.md    | 21 +++++++--
 docs/dynamic_point_aggregation/README.md      |  4 ++
 .../dynamic_interval_management.md            | 10 +++--
 .../dynamic_point_aggregation.md              |  6 +--
 .../suffix_pattern_recognition.md             |  4 +-
 docs/suffix_pattern_recognition/README.md     |  4 ++
 mkdocs.yml                                    |  7 ++-
 pyproject.toml                                |  1 +
 uv.lock                                       |  2 +
 10 files changed, 43 insertions(+), 59 deletions(-)
 delete mode 100644 docs/development.md
 rename docs/{ => modules}/dynamic_interval_management.md (96%)
 rename docs/{ => modules}/dynamic_point_aggregation.md (95%)
 rename docs/{ => modules}/suffix_pattern_recognition.md (94%)

diff --git a/docs/development.md b/docs/development.md
deleted file mode 100644
index ddf30cf..0000000
--- a/docs/development.md
+++ /dev/null
@@ -1,43 +0,0 @@
-
-data_streaming_accelerators/
-├── .github/workflows/
-├── docs/
-│   └── mkdocs.yml
-├── src/
-│   └── data_streaming_accelerators/
-│       ├── __init__.py
-│       ├── __main__.py
-│       ├── core/
-│       |   ├── dynamic_interval_management.py
-│       |   ├── dynamic_point_aggregation.py
-│       |   └── suffix_pattern_recognition.py
-│       ├── api.py
-├── tests/
-│   ├── conftest.py
-│   ├── test_api.py
-│   ├── test_core.py
-├── .gitignore
-├── pyproject.toml
-├── README.md
-└── LICENSE
-
-```sh
-# https://docs.astral.sh/uv/getting-started/installation/
-# install uv from official installer
-wget -qO- https://astral.sh/uv/install.sh | sh
-```
-
-```
-# Run specific markers in pytest
-uv run --group dev --extra benchmark pytest -sv -m func
-uv run --group dev --extra benchmark pytest -sv -m perf
-
-# Run pytest
-uv run --group dev --extra benchmark pytest -sv
-
-# Watch run until it completes.
-gh run watch
-
-# Show project files.
-(git ls-files | xargs tail -n +1) 2>&1 >var/files.txt
-```
diff --git a/docs/dynamic_interval_management/README.md b/docs/dynamic_interval_management/README.md
index 39f467c..2fb0287 100644
--- a/docs/dynamic_interval_management/README.md
+++ b/docs/dynamic_interval_management/README.md
@@ -21,7 +21,7 @@ The advantage of an Augmented AVL Interval Tree is its ability to prune search b
 
 ## 2. Design Approaches
 
-### Optimal Approaches for Batch Data (Static Intervals)
+## Optimal Approaches for Batch Data (Static Intervals)
 * **Sweep-line (Variant 1):** Uses a sorted list of edge objects and a counter.
     * **Complexity (Batch):** $O(N \log N)$ setup, $O(N)$ calculation. 
     * **Complexity (Streaming):** $O(N \log N)$ per `insert`/`put` operation.
@@ -31,7 +31,7 @@ The advantage of an Augmented AVL Interval Tree is its ability to prune search b
     * **Complexity (Streaming):** $O(N \log N)$ per `insert`/`put` operation.
     * **Verdict:** Suitable for batch case due to best-in-class ~7ms benchmark with static intervals. Not suitable for streaming case due to high complexity.
 
-### Optimal Approaches for Streaming Data (Dynamic Intervals)
+## Optimal Approaches for Streaming Data (Dynamic Intervals)
 * **Augmented AVL Interval Tree (Variant 3):** A stateful, self-balancing BST.
     * **Complexity (Batch):** $O(N \log N)$ setup, $O(N)$ calculation. 
     * **Complexity (Streaming):** $O(\log N)$ per `insert`/`put` operation.
@@ -67,4 +67,19 @@ To ensure system reliability during high-frequency updates, I prioritized **Corr
 By implementing a **Sentinel Node Architecture** with a **Two-Down** AVL balancing subtree rotation strategy and removing the need for sentinel node checks throughout the codebase, I simplified the balancing feature and provided a cleaner and more maintainable implementation.
 
 ### Python Object-Model Tuning
-To reduce object-overhead due to the Python object-model, I implemented **Attribute Flattening**. After replacing packed collections (`self.interval[0]`) with discrete integers (`self.lo`, `self.hi`), I reduced constant factors in the hot execution path and achieved a **15% reduction** in benchmarks with static intervals.
+To reduce object-overhead due to the Python object-model, I implemented **Attribute Flattening**. After replacing packed collections (`self.interval[0]`) with discrete integers (`self.lo`, `self.hi`), I reduced constant factors in the hot execution path and achieved a **15% reduction** in benchmarks with static intervals. 123
+
+test
+
+## 5. Getting Started
+
+This design requires **Python 3.13+**.
+
+To run the regression tests for this design:
+```bash
+uv run --group dev --extra benchmark pytest -sv
+```
+
+## 6. API Reference
+
+::: data_streaming_accelerators.core.dynamic_interval_management
diff --git a/docs/dynamic_point_aggregation/README.md b/docs/dynamic_point_aggregation/README.md
index 32a0bc8..89563e8 100644
--- a/docs/dynamic_point_aggregation/README.md
+++ b/docs/dynamic_point_aggregation/README.md
@@ -83,3 +83,7 @@ These results highlight that the batch variant (V1) is suitable for smaller data
 
 ### State Transitions
 To ensure new point values are correctly merged with existing disjoint intervals, I applied **Correctness by Design** by separately handling the 3 overlap cases: the enclosed-by case (early exit if lower and upper bounds at insertion point are already aligned), the adjacent-to case (join with 1 or 2 neighbors if lower and upper bounds at insertion point are adjacent), and the distinct-from case (insert as new lower and upper bounds).
+
+## 5. API Reference
+
+::: data_streaming_accelerators.core.dynamic_point_aggregation
diff --git a/docs/dynamic_interval_management.md b/docs/modules/dynamic_interval_management.md
similarity index 96%
rename from docs/dynamic_interval_management.md
rename to docs/modules/dynamic_interval_management.md
index 325d0a3..2fb0287 100644
--- a/docs/dynamic_interval_management.md
+++ b/docs/modules/dynamic_interval_management.md
@@ -17,7 +17,7 @@ The theoretical lower bound for merging $N$ static intervals is $\Omega(N \log N
 
 The advantage of an Augmented AVL Interval Tree is its ability to prune search branches that cannot contain an overlap, ensuring $O(\log N)$ search time.
 
-![Diagram of Pruning Logic](dynamic_interval_management/static/pruning-diagram.png)
+![Diagram of Pruning Logic](static/pruning-diagram.png)
 
 ## 2. Design Approaches
 
@@ -53,7 +53,7 @@ In benchmarks with dynamic intervals up to $N=3000$, the Interval Tree (Variant
 | 2000 | 0.6743 | 0.0383 | 17.6x |
 | 3000 | 1.6093 | 0.0318 | **50.6x** |
 
-![Graph for Performance Report](dynamic_interval_management/static/performance-report-1280x640.png)
+![Graph for Performance Report](static/performance-report-1280x640.png)
 
 ## 4. Design Optimizations
 
@@ -67,7 +67,9 @@ To ensure system reliability during high-frequency updates, I prioritized **Corr
 By implementing a **Sentinel Node Architecture** with a **Two-Down** AVL balancing subtree rotation strategy and removing the need for sentinel node checks throughout the codebase, I simplified the balancing feature and provided a cleaner and more maintainable implementation.
 
 ### Python Object-Model Tuning
-To reduce object-overhead due to the Python object-model, I implemented **Attribute Flattening**. After replacing packed collections (`self.interval[0]`) with discrete integers (`self.lo`, `self.hi`), I reduced constant factors in the hot execution path and achieved a **15% reduction** in benchmarks with static intervals.
+To reduce object-overhead due to the Python object-model, I implemented **Attribute Flattening**. After replacing packed collections (`self.interval[0]`) with discrete integers (`self.lo`, `self.hi`), I reduced constant factors in the hot execution path and achieved a **15% reduction** in benchmarks with static intervals. 123
+
+test
 
 ## 5. Getting Started
 
@@ -80,4 +82,4 @@ uv run --group dev --extra benchmark pytest -sv
 
 ## 6. API Reference
 
-::: data_streaming_accelerators.core.dynamic_interval_management.DynamicIntervalManagementV3
+::: data_streaming_accelerators.core.dynamic_interval_management
diff --git a/docs/dynamic_point_aggregation.md b/docs/modules/dynamic_point_aggregation.md
similarity index 95%
rename from docs/dynamic_point_aggregation.md
rename to docs/modules/dynamic_point_aggregation.md
index c26e267..89563e8 100644
--- a/docs/dynamic_point_aggregation.md
+++ b/docs/modules/dynamic_point_aggregation.md
@@ -32,11 +32,11 @@ With python `sortedcontainers`, these runtime complexities were instead $O(N \sq
 ### Streaming Benchmark Results
 When the request traffic was mostly `put` requests (R=0.1) to simulate offline scenarios, the batch variant (V1) was 2.7x faster when data size was smaller (N=100) and the streaming variant was **4.9x faster** when data size was larger (N=50000).
 
-![Speedup by Data Size (R=0.1)](dynamic_point_aggregation/static/speedup_by_data_size_request_distr0.1.png)
+![Speedup by Data Size (R=0.1)](static/speedup_by_data_size_request_distr0.1.png)
 
 When the request traffic was balanced beween `put` and `get` requests (R=0.5) to simulate online scenarios, the batch variant (V1) was **1.2x faster** when data size was smaller (N=100) and the streaming variant was **6.4x faster** when data size was larger (N=50000).
 
-![Speedup by Data Size (R=0.5)](dynamic_point_aggregation/static/speedup_by_data_size_request_distr0.5.png)
+![Speedup by Data Size (R=0.5)](static/speedup_by_data_size_request_distr0.5.png)
 
 These results highlight that the batch variant (V1) is suitable for smaller data streams and offline scenarios, whereas the streaming variant (V2) is suitable for larger data streams and online scenarios.
 
@@ -86,4 +86,4 @@ To ensure new point values are correctly merged with existing disjoint intervals
 
 ## 5. API Reference
 
-::: data_streaming_accelerators.core.dynamic_point_aggregation.DynamicPointAggregationV2
+::: data_streaming_accelerators.core.dynamic_point_aggregation
diff --git a/docs/suffix_pattern_recognition.md b/docs/modules/suffix_pattern_recognition.md
similarity index 94%
rename from docs/suffix_pattern_recognition.md
rename to docs/modules/suffix_pattern_recognition.md
index 72c5289..3e87ae9 100644
--- a/docs/suffix_pattern_recognition.md
+++ b/docs/modules/suffix_pattern_recognition.md
@@ -19,7 +19,7 @@ For batch data (offline scenario), reading the query pattern from a static array
 
 The advantage of reverse-traversal prefix tree search is that it can check multiple suffix patterns at once, ensuring $O(W)$ query time (and is independent of the suffix pattern count $K$ and the query pattern length $N$). This is possible because of reverse encoding.
 
-![Diagram for reverse encoding](suffix_pattern_recognition/static/diagram-image.png)
+![Diagram for reverse encoding](static/diagram-image.png)
 
 ## 2. Design Approaches & Trade-offs
 
@@ -31,4 +31,4 @@ To reduce object-overhead due to the Python object-model, I implemented a **nest
 
 ## 3. API Reference
 
-::: data_streaming_accelerators.core.suffix_pattern_recognition.SuffixPatternRecognitionV1
+::: data_streaming_accelerators.core.suffix_pattern_recognition
diff --git a/docs/suffix_pattern_recognition/README.md b/docs/suffix_pattern_recognition/README.md
index 58f08ed..3e87ae9 100644
--- a/docs/suffix_pattern_recognition/README.md
+++ b/docs/suffix_pattern_recognition/README.md
@@ -28,3 +28,7 @@ Although Direct Search (v1) requires ~90% less lines of code, it performs worse
 
 ### Python Object-Model Tuning
 To reduce object-overhead due to the Python object-model, I implemented a **nested hash map** for the reverse-traversal prefix tree, with each "node" using a character for the hash map key and a reference to the next "node" for the hash map value. This approach reduced object lookup during queries.
+
+## 3. API Reference
+
+::: data_streaming_accelerators.core.suffix_pattern_recognition
diff --git a/mkdocs.yml b/mkdocs.yml
index 644ded1..01040e8 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -29,7 +29,6 @@ plugins:
 nav:
   - Overview: index.md
   - Modules:
-    - Dynamic Interval Management: dynamic_interval_management.md
-    - Dynamic Point Aggregation: dynamic_point_aggregation.md
-    - Suffix Pattern Recognition: suffix_pattern_recognition.md
-  - Development: development.md
+    - Dynamic Interval Management: modules/dynamic_interval_management.md
+    - Dynamic Point Aggregation: modules/dynamic_point_aggregation.md
+    - Suffix Pattern Recognition: modules/suffix_pattern_recognition.md
diff --git a/pyproject.toml b/pyproject.toml
index 2157f86..e1bcda6 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -19,6 +19,7 @@ dev = [
 docs = [
     "mkdocs-material>=9.7.6",
     "mkdocs-mermaid2-plugin>=1.2.3",
+    "mkdocstrings-python>=2.0.3",
     "mkdocstrings[python]>=1.0.4",
 ]
 lint = [
diff --git a/uv.lock b/uv.lock
index 62730d8..df95116 100644
--- a/uv.lock
+++ b/uv.lock
@@ -218,6 +218,7 @@ docs = [
     { name = "mkdocs-material" },
     { name = "mkdocs-mermaid2-plugin" },
     { name = "mkdocstrings", extra = ["python"] },
+    { name = "mkdocstrings-python" },
 ]
 lint = [
     { name = "ruff" },
@@ -237,6 +238,7 @@ docs = [
     { name = "mkdocs-material", specifier = ">=9.7.6" },
     { name = "mkdocs-mermaid2-plugin", specifier = ">=1.2.3" },
     { name = "mkdocstrings", extras = ["python"], specifier = ">=1.0.4" },
+    { name = "mkdocstrings-python", specifier = ">=2.0.3" },
 ]
 lint = [{ name = "ruff", specifier = ">=0.15.12" }]
 

From a35138c8a585df6d1119b7ff9a6a0b9c23eedab7 Mon Sep 17 00:00:00 2001
From: achekery <6503526+achekery@users.noreply.github.com>
Date: Tue, 12 May 2026 18:23:08 -0700
Subject: [PATCH 04/12] dev notes

---
 DEVELOPMENT.md | 46 ++++++++++------------------------------------
 1 file changed, 10 insertions(+), 36 deletions(-)

diff --git a/DEVELOPMENT.md b/DEVELOPMENT.md
index ddf30cf..9631ca3 100644
--- a/DEVELOPMENT.md
+++ b/DEVELOPMENT.md
@@ -1,43 +1,17 @@
+# DEVELOPMENT
 
-data_streaming_accelerators/
-├── .github/workflows/
-├── docs/
-│   └── mkdocs.yml
-├── src/
-│   └── data_streaming_accelerators/
-│       ├── __init__.py
-│       ├── __main__.py
-│       ├── core/
-│       |   ├── dynamic_interval_management.py
-│       |   ├── dynamic_point_aggregation.py
-│       |   └── suffix_pattern_recognition.py
-│       ├── api.py
-├── tests/
-│   ├── conftest.py
-│   ├── test_api.py
-│   ├── test_core.py
-├── .gitignore
-├── pyproject.toml
-├── README.md
-└── LICENSE
+TODO: Verify gh-deploy workflow is successful
 
-```sh
-# https://docs.astral.sh/uv/getting-started/installation/
-# install uv from official installer
-wget -qO- https://astral.sh/uv/install.sh | sh
-```
+TODO: Verify mkdocs generation is successful
 
 ```
-# Run specific markers in pytest
-uv run --group dev --extra benchmark pytest -sv -m func
-uv run --group dev --extra benchmark pytest -sv -m perf
-
-# Run pytest
-uv run --group dev --extra benchmark pytest -sv
+uv run mkdocs serve -v
+```
 
-# Watch run until it completes.
-gh run watch
+TODO: Remove unnecessary files
 
-# Show project files.
-(git ls-files | xargs tail -n +1) 2>&1 >var/files.txt
+```
+rm -rf docs/dynamic_interval_management/
+rm -rf docs/dynamic_point_aggregation/
+rm -rf docs/suffix_pattern_recognition/
 ```

From dc674947528c0b9b14953ecb74f45ccad7ce880a Mon Sep 17 00:00:00 2001
From: achekery <6503526+achekery@users.noreply.github.com>
Date: Tue, 12 May 2026 21:31:18 -0700
Subject: [PATCH 05/12] add mkdocs commands

---
 .github/workflows/docs.yml       | 21 +++++++++++++--------
 .github/workflows/python-app.yml |  4 ++--
 DEVELOPMENT.md                   | 26 ++++++++++++++++++++++++++
 3 files changed, 41 insertions(+), 10 deletions(-)

diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml
index 52eeb2d..13adc64 100644
--- a/.github/workflows/docs.yml
+++ b/.github/workflows/docs.yml
@@ -6,13 +6,18 @@ on:
 jobs:
   deploy:
     runs-on: ubuntu-latest
+
     steps:
-      - uses: actions/checkout@v4
-      - name: Install uv
-        uses: astral-sh/setup-uv@v3
-      - name: Setup Python
-        run: uv python install 3.13
-      - name: Build and Deploy
+      - uses: actions/checkout@v6
+
+      - name: Setup python
+        uses: actions/setup-python@v6
+        with:
+          python-version-file: "pyproject.toml"
+
+      - name: Setup uv
+        uses: astral-sh/setup-uv@08807647e7069bb48b6ef5acd8ec9567f424441b # v8.1.0
+
+      - name: Build docs with mkdocs
         run: |
-          uv sync --group docs
-          uv run mkdocs gh-deploy --force
+          uv run --group docs mkdocs gh-deploy -v --clean --strict --force
diff --git a/.github/workflows/python-app.yml b/.github/workflows/python-app.yml
index 108f319..f90c226 100644
--- a/.github/workflows/python-app.yml
+++ b/.github/workflows/python-app.yml
@@ -24,11 +24,11 @@ jobs:
     - name: Setup uv
       uses: astral-sh/setup-uv@08807647e7069bb48b6ef5acd8ec9567f424441b # v8.1.0
 
-    - name: Run pytest
+    - name: Run tests with pytest
       run: |
         uv run --group dev --extra benchmark pytest -sv
 
-    - name: Upload artifacts
+    - name: Upload artifacts from package tests
       uses: actions/upload-artifact@v4
       with:
         name: artifacts
diff --git a/DEVELOPMENT.md b/DEVELOPMENT.md
index 9631ca3..161444a 100644
--- a/DEVELOPMENT.md
+++ b/DEVELOPMENT.md
@@ -15,3 +15,29 @@ rm -rf docs/dynamic_interval_management/
 rm -rf docs/dynamic_point_aggregation/
 rm -rf docs/suffix_pattern_recognition/
 ```
+
+## Run tests with pytest
+
+```sh
+# Option 1: All tests [Default]
+uv run --group dev --extra benchmark pytest -sv
+
+# Option 2: Functional tests only
+uv run --group dev --extra benchmark pytest -sv -m func
+
+# Option 3: Performance tests only
+uv run --group dev --extra benchmark pytest -sv -m perf
+```
+
+## Build docs with mkdocs
+
+```sh
+# Option 1: Build and deploy [Default]
+uv run --group docs mkdocs gh-deploy -v --clean --strict --force
+
+# Option 2: Build only
+uv run --group docs mkdocs build -v --clean --strict
+
+# Option 3: Deploy only using local server
+uv run --group docs mkdocs serve -v --clean --strict
+```

From 902b90c4e81b925dbb028159c96b93abdaad4ef9 Mon Sep 17 00:00:00 2001
From: achekery <6503526+achekery@users.noreply.github.com>
Date: Tue, 12 May 2026 22:16:44 -0700
Subject: [PATCH 06/12] add macros expansion in mkdocs

---
 docs/modules/dynamic_interval_management.md   |  85 -----------------
 .../dynamic_interval_management/README.md     |   4 +-
 .../static/performance-report-1280x640.png    | Bin
 .../static/pruning-diagram.png                | Bin
 .../static/pruning-mermaid.txt                |   0
 docs/modules/dynamic_point_aggregation.md     |  89 ------------------
 .../dynamic_point_aggregation/README.md       |   0
 .../speedup_by_data_size_request_distr0.1.png | Bin
 .../speedup_by_data_size_request_distr0.5.png | Bin
 docs/modules/suffix_pattern_recognition.md    |  34 -------
 .../suffix_pattern_recognition/README.md      |   4 +-
 .../static/diagram-image.png                  | Bin
 .../static/diagram-mermaid.txt                |   0
 mkdocs.yml                                    |   8 +-
 pyproject.toml                                |   1 +
 uv.lock                                       |  53 +++++++++++
 16 files changed, 65 insertions(+), 213 deletions(-)
 delete mode 100644 docs/modules/dynamic_interval_management.md
 rename docs/{ => modules}/dynamic_interval_management/README.md (98%)
 rename docs/{ => modules}/dynamic_interval_management/static/performance-report-1280x640.png (100%)
 rename docs/{ => modules}/dynamic_interval_management/static/pruning-diagram.png (100%)
 rename docs/{ => modules}/dynamic_interval_management/static/pruning-mermaid.txt (100%)
 delete mode 100644 docs/modules/dynamic_point_aggregation.md
 rename docs/{ => modules}/dynamic_point_aggregation/README.md (100%)
 rename docs/{ => modules}/dynamic_point_aggregation/static/speedup_by_data_size_request_distr0.1.png (100%)
 rename docs/{ => modules}/dynamic_point_aggregation/static/speedup_by_data_size_request_distr0.5.png (100%)
 delete mode 100644 docs/modules/suffix_pattern_recognition.md
 rename docs/{ => modules}/suffix_pattern_recognition/README.md (97%)
 rename docs/{ => modules}/suffix_pattern_recognition/static/diagram-image.png (100%)
 rename docs/{ => modules}/suffix_pattern_recognition/static/diagram-mermaid.txt (100%)

diff --git a/docs/modules/dynamic_interval_management.md b/docs/modules/dynamic_interval_management.md
deleted file mode 100644
index 2fb0287..0000000
--- a/docs/modules/dynamic_interval_management.md
+++ /dev/null
@@ -1,85 +0,0 @@
-# Dynamic Interval Management
-![Python CI](https://github.com/achekery/data-streaming/actions/workflows/python-app.yml/badge.svg)
-
-## 1. Design Summary
-The theoretical lower bound for merging $N$ static intervals is $\Omega(N \log N)$ due to the sorting requirement. By focusing on interval edges rather than the source intervals themselves, we can focus on efficient algorithms with compact implementation.  However, in **Online Streaming Environments**, the task shifts from batch data loading (static intervals) to streaming data ingestion (dynamic intervals).
-
-### 📊 Complexity Analysis
-
-| Operation | Batch Variants (v1/v2) | Streaming Variant (v3) | Comparison |
-| :--- | :--- | :--- | :--- |
-| **Initial Setup** | $O(N \log N)$ | $O(N \log N)$ | Equivalent |
-| **Batch Updates (N)** | $O(N \log N)$ | $O(N \log N)$ | Equivalent |
-| **Streaming Updates (1)** | $O(N \log N)$ | **$O(\log N)$** | **Streaming Variant** is superior |
-| **Space Complexity** | $O(N)$ | $O(N)$ | Equivalent |
-
-### 🚀 The Pruning Logic (Visual)
-
-The advantage of an Augmented AVL Interval Tree is its ability to prune search branches that cannot contain an overlap, ensuring $O(\log N)$ search time.
-
-![Diagram of Pruning Logic](static/pruning-diagram.png)
-
-## 2. Design Approaches
-
-## Optimal Approaches for Batch Data (Static Intervals)
-* **Sweep-line (Variant 1):** Uses a sorted list of edge objects and a counter.
-    * **Complexity (Batch):** $O(N \log N)$ setup, $O(N)$ calculation. 
-    * **Complexity (Streaming):** $O(N \log N)$ per `insert`/`put` operation.
-    * **Verdict:** Suitable for batch case due to second-best ~16ms benchmark with static intervals impacted by object-overhead during calculation. Not suitable for streaming case due to high complexity.
-* **Two-Pointer Search (Variant 2):** Uses two sorted edge arrays and two pointers.
-    * **Complexity (Batch):** $O(N \log N)$ setup, $O(N)$ calculation.
-    * **Complexity (Streaming):** $O(N \log N)$ per `insert`/`put` operation.
-    * **Verdict:** Suitable for batch case due to best-in-class ~7ms benchmark with static intervals. Not suitable for streaming case due to high complexity.
-
-## Optimal Approaches for Streaming Data (Dynamic Intervals)
-* **Augmented AVL Interval Tree (Variant 3):** A stateful, self-balancing BST.
-    * **Complexity (Batch):** $O(N \log N)$ setup, $O(N)$ calculation. 
-    * **Complexity (Streaming):** $O(\log N)$ per `insert`/`put` operation.
-    * **Verdict:** Not suitable for batch case due to poor ~4130ms benchmark with static intervals impacted by object-overhead during calculation. Suitable for streaming case due to best-in-class complexity per `insert`/`put` operation. Notice the optimal approaches for batch data merging are easier to maintain, with **90% fewer LOC** (~25 vs ~250)! 
-
-## 3. Design Trade-offs
-
-### The Efficiency Paradox
-In benchmarks with static intervals, the Two-Pointer Search (Variant 2) was **400x faster** than the Interval Tree (Variant 3). However, in **Online Streaming Environments**, the Two-Pointer Search overall complexity degrades to $O(N^2 \log N)$ over a series of $N$ updates while the Interval Tree overall complexity maintains $O(N \log N)$.
-
-### Streaming Benchmark Results
-In benchmarks with dynamic intervals up to $N=3000$, the Interval Tree (Variant 3) was as much as **50x faster** than the Two-Pointer Search (Variant 2).  While the Two-Pointer Search (Variant 2) is faster for a single batch run, it fails to scale in an **Online Streaming Environment** where the merged state must be updated for every new interval. As $N$ increases, the Two-Pointer Search runtime explodes quadratically while the Interval Tree runtime continues linearly.
-
-| Input Size (N) | Batch-Style (s) | Tree-Style (s) | Speedup |
-| :--- | :--- | :--- | :--- |
-| 100 | 0.0015 | 0.0021 | 0.7x |
-| 500 | 0.0359 | 0.0140 | 2.6x |
-| 1000 | 0.1501 | 0.0230 | 6.5x |
-| 2000 | 0.6743 | 0.0383 | 17.6x |
-| 3000 | 1.6093 | 0.0318 | **50.6x** |
-
-![Graph for Performance Report](static/performance-report-1280x640.png)
-
-## 4. Design Optimizations
-
-### Augmented Metadata
-By augmenting the BST with `subtree_max` metadata, I reduced the search-and-merge task from a linear scan to a logarithmic search. This allows the streaming platform to maintain a "Live" merged state with $O(\log N)$ latency per request.
-
-### Invariant-Driven Correctness
-To ensure system reliability during high-frequency updates, I prioritized **Correctness by Design** by explicitly maintaining the AVL balance and metadata invariants during every mutation (`insert`, `delete`).
-
-### Architectural Hardening
-By implementing a **Sentinel Node Architecture** with a **Two-Down** AVL balancing subtree rotation strategy and removing the need for sentinel node checks throughout the codebase, I simplified the balancing feature and provided a cleaner and more maintainable implementation.
-
-### Python Object-Model Tuning
-To reduce object-overhead due to the Python object-model, I implemented **Attribute Flattening**. After replacing packed collections (`self.interval[0]`) with discrete integers (`self.lo`, `self.hi`), I reduced constant factors in the hot execution path and achieved a **15% reduction** in benchmarks with static intervals. 123
-
-test
-
-## 5. Getting Started
-
-This design requires **Python 3.13+**.
-
-To run the regression tests for this design:
-```bash
-uv run --group dev --extra benchmark pytest -sv
-```
-
-## 6. API Reference
-
-::: data_streaming_accelerators.core.dynamic_interval_management
diff --git a/docs/dynamic_interval_management/README.md b/docs/modules/dynamic_interval_management/README.md
similarity index 98%
rename from docs/dynamic_interval_management/README.md
rename to docs/modules/dynamic_interval_management/README.md
index 2fb0287..680b648 100644
--- a/docs/dynamic_interval_management/README.md
+++ b/docs/modules/dynamic_interval_management/README.md
@@ -17,7 +17,9 @@ The theoretical lower bound for merging $N$ static intervals is $\Omega(N \log N
 
 The advantage of an Augmented AVL Interval Tree is its ability to prune search branches that cannot contain an overlap, ensuring $O(\log N)$ search time.
 
-![Diagram of Pruning Logic](static/pruning-diagram.png)
+```mermaid
+{% include "modules/dynamic_interval_management/static/pruning-mermaid.txt" %}
+```
 
 ## 2. Design Approaches
 
diff --git a/docs/dynamic_interval_management/static/performance-report-1280x640.png b/docs/modules/dynamic_interval_management/static/performance-report-1280x640.png
similarity index 100%
rename from docs/dynamic_interval_management/static/performance-report-1280x640.png
rename to docs/modules/dynamic_interval_management/static/performance-report-1280x640.png
diff --git a/docs/dynamic_interval_management/static/pruning-diagram.png b/docs/modules/dynamic_interval_management/static/pruning-diagram.png
similarity index 100%
rename from docs/dynamic_interval_management/static/pruning-diagram.png
rename to docs/modules/dynamic_interval_management/static/pruning-diagram.png
diff --git a/docs/dynamic_interval_management/static/pruning-mermaid.txt b/docs/modules/dynamic_interval_management/static/pruning-mermaid.txt
similarity index 100%
rename from docs/dynamic_interval_management/static/pruning-mermaid.txt
rename to docs/modules/dynamic_interval_management/static/pruning-mermaid.txt
diff --git a/docs/modules/dynamic_point_aggregation.md b/docs/modules/dynamic_point_aggregation.md
deleted file mode 100644
index 89563e8..0000000
--- a/docs/modules/dynamic_point_aggregation.md
+++ /dev/null
@@ -1,89 +0,0 @@
-# Dynamic Point Aggregation
-![Python CI](https://github.com/achekery/data-streaming/actions/workflows/python-app.yml/badge.svg)
-
-## 1. Design Summary
-The optimal runtime complexity for dynamic point aggregation from $N$ point values to $O(N)$ disjoint intervals is $\Omega(N \log N)$ due to the ordering requirement. The request handler uses `put` requests to add new values and `get` requests to make a new interval sequence.
-
-Because offline scenarios (batch data) have known usage patterns, the batch variant (V1) can **optimize the hot path** by simplifying high-usage `put` requests to $O(1)$ and expanding low-usage `get` requests to $O(N \log N)$.
-
-However, because online scenarios (streaming data) do not have known usage patterns, the streaming variant (V2) must instead **balance complexity** between `put` requests ($O(\log N)$) and `get` requests ($O(N)$).
-
-### 📊 Complexity Analysis
-
-| Operation | Batch Variant (V1) | Streaming Variant (V2) | Comparison |
-| :--- | :--- | :--- | :--- |
-| **Initial Setup** | $O(1)$ | $O(1)$ | Equivalent |
-| **Batch Updates (N Put, 1 Get)** | $O(N \log N)$ | $O(N \log N)$ | Equivalent |
-| **Streaming Updates (N Put, K Get)** | $O(K*N \log N)$ | $O(N \log N + K * N)$ | **V2 is Superior** |
-| **Space Complexity** | $O(N)$ | $O(N)$ | Equivalent
-
-## 2. Design Details
-The batch variant (V1) uses an unordered set to add new values as data points in $O(1)$ per `put` request and does one pass over a new sorted list with sweep line method to generate disjoint intervals in $O(N \log N)$ per `get` request.
-
-The streaming variant (V2) uses two sorted sets with binary search to add new values as interval bounds in $O(\log N)$ per `put` request (or $O(\sqrt N)$ with python `sortedcontainers`) and does one pass over the existing sorted sets with sweep line method to generate disjoint intervals in $O(N)$ per `get` request.
-
-## 3. Design Trade-offs
-
-### The Efficiency Paradox
-Although the batch variant (V1) was **2.7x faster** in small-scale offline scenarios (N=100, R=0.1), the streaming variant (V2) was **6.4x faster** in large-scale online scenarios (N=50000, R=0.5). This performance gain in online scenarios was due to the runtime complexity of the streaming variant at $O(N \log N + K*N)$ increasing more slowly with data size compared to the batch variant at $O(K*N \log N)$.
-
-With python `sortedcontainers`, these runtime complexities were instead $O(N \sqrt N + K*N)$ and $O(K*N \log N)$ respectively. Although the streaming variant was still faster, the performance gain was less dramatic since $O(\sqrt N)$ increases faster than $O(\log N)$.
-
-### Streaming Benchmark Results
-When the request traffic was mostly `put` requests (R=0.1) to simulate offline scenarios, the batch variant (V1) was 2.7x faster when data size was smaller (N=100) and the streaming variant was **4.9x faster** when data size was larger (N=50000).
-
-![Speedup by Data Size (R=0.1)](static/speedup_by_data_size_request_distr0.1.png)
-
-When the request traffic was balanced beween `put` and `get` requests (R=0.5) to simulate online scenarios, the batch variant (V1) was **1.2x faster** when data size was smaller (N=100) and the streaming variant was **6.4x faster** when data size was larger (N=50000).
-
-![Speedup by Data Size (R=0.5)](static/speedup_by_data_size_request_distr0.5.png)
-
-These results highlight that the batch variant (V1) is suitable for smaller data streams and offline scenarios, whereas the streaming variant (V2) is suitable for larger data streams and online scenarios.
-
-| TestCaseID | DataSize | RequestDistribution | V1TimeElapsed | V2TimeElapsed | SpeedupV1V2 | SpeedupV2V1 |
-| :--- | :--- | :--- | :--- | :--- | :--- | :--- |
-| 0 | 100 | 0.100 | 0.000 | 0.001 | 2.706 | 0.370 |
-| 1 | 100 | 0.200 | 0.000 | 0.001 | 1.998 | 0.500 |
-| 2 | 100 | 0.500 | 0.001 | 0.001 | 1.289 | 0.776 |
-| 3 | 100 | 0.800 | 0.002 | 0.003 | 1.042 | 0.960 |
-| 4 | 200 | 0.100 | 0.001 | 0.001 | 2.115 | 0.473 |
-| 5 | 200 | 0.200 | 0.001 | 0.001 | 1.642 | 0.609 |
-| 6 | 200 | 0.500 | 0.003 | 0.003 | 1.010 | 0.990 |
-| 7 | 200 | 0.800 | 0.013 | 0.010 | 0.821 | 1.218 |
-| 8 | 500 | 0.100 | 0.002 | 0.003 | 1.606 | 0.623 |
-| 9 | 500 | 0.200 | 0.004 | 0.005 | 1.116 | 0.896 |
-| 10 | 500 | 0.500 | 0.020 | 0.016 | 0.816 | 1.226 |
-| 11 | 500 | 0.800 | 0.071 | 0.051 | 0.726 | 1.378 |
-| 12 | 1000 | 0.100 | 0.008 | 0.009 | 1.059 | 0.944 |
-| 13 | 1000 | 0.200 | 0.016 | 0.014 | 0.861 | 1.162 |
-| 14 | 1000 | 0.500 | 0.070 | 0.050 | 0.715 | 1.400 |
-| 15 | 1000 | 0.800 | 0.273 | 0.186 | 0.680 | 1.471 |
-| 16 | 2000 | 0.100 | 0.028 | 0.025 | 0.920 | 1.087 |
-| 17 | 2000 | 0.200 | 0.059 | 0.046 | 0.776 | 1.289 |
-| 18 | 2000 | 0.500 | 0.236 | 0.159 | 0.671 | 1.489 |
-| 19 | 2000 | 0.800 | 1.002 | 0.651 | 0.650 | 1.538 |
-| 20 | 5000 | 0.100 | 0.140 | 0.105 | 0.751 | 1.331 |
-| 21 | 5000 | 0.200 | 0.326 | 0.216 | 0.663 | 1.509 |
-| 22 | 5000 | 0.500 | 1.251 | 0.735 | 0.587 | 1.703 |
-| 23 | 5000 | 0.800 | 5.099 | 3.020 | 0.592 | 1.688 |
-| 24 | 10000 | 0.100 | 0.466 | 0.266 | 0.572 | 1.748 |
-| 25 | 10000 | 0.200 | 1.031 | 0.541 | 0.525 | 1.906 |
-| 26 | 10000 | 0.500 | 4.038 | 1.950 | 0.483 | 2.071 |
-| 27 | 10000 | 0.800 | 15.824 | 7.414 | 0.469 | 2.134 |
-| 28 | 20000 | 0.100 | 1.198 | 0.504 | 0.421 | 2.376 |
-| 29 | 20000 | 0.200 | 2.633 | 0.990 | 0.376 | 2.660 |
-| 30 | 20000 | 0.500 | 10.557 | 3.617 | 0.343 | 2.919 |
-| 31 | 20000 | 0.800 | 42.168 | 14.237 | 0.338 | 2.962 |
-| 32 | 50000 | 0.100 | 3.473 | 0.695 | 0.200 | 4.996 |
-| 33 | 50000 | 0.200 | 7.765 | 1.349 | 0.174 | 5.757 |
-| 34 | 50000 | 0.500 | 30.483 | 4.756 | 0.156 | 6.410 |
-| 35 | 50000 | 0.800 | 122.369 | 19.013 | 0.155 | 6.436 |
-
-## 4. Design Optimizations
-
-### State Transitions
-To ensure new point values are correctly merged with existing disjoint intervals, I applied **Correctness by Design** by separately handling the 3 overlap cases: the enclosed-by case (early exit if lower and upper bounds at insertion point are already aligned), the adjacent-to case (join with 1 or 2 neighbors if lower and upper bounds at insertion point are adjacent), and the distinct-from case (insert as new lower and upper bounds).
-
-## 5. API Reference
-
-::: data_streaming_accelerators.core.dynamic_point_aggregation
diff --git a/docs/dynamic_point_aggregation/README.md b/docs/modules/dynamic_point_aggregation/README.md
similarity index 100%
rename from docs/dynamic_point_aggregation/README.md
rename to docs/modules/dynamic_point_aggregation/README.md
diff --git a/docs/dynamic_point_aggregation/static/speedup_by_data_size_request_distr0.1.png b/docs/modules/dynamic_point_aggregation/static/speedup_by_data_size_request_distr0.1.png
similarity index 100%
rename from docs/dynamic_point_aggregation/static/speedup_by_data_size_request_distr0.1.png
rename to docs/modules/dynamic_point_aggregation/static/speedup_by_data_size_request_distr0.1.png
diff --git a/docs/dynamic_point_aggregation/static/speedup_by_data_size_request_distr0.5.png b/docs/modules/dynamic_point_aggregation/static/speedup_by_data_size_request_distr0.5.png
similarity index 100%
rename from docs/dynamic_point_aggregation/static/speedup_by_data_size_request_distr0.5.png
rename to docs/modules/dynamic_point_aggregation/static/speedup_by_data_size_request_distr0.5.png
diff --git a/docs/modules/suffix_pattern_recognition.md b/docs/modules/suffix_pattern_recognition.md
deleted file mode 100644
index 3e87ae9..0000000
--- a/docs/modules/suffix_pattern_recognition.md
+++ /dev/null
@@ -1,34 +0,0 @@
-# Suffix Pattern Recognition
-![Python CI](https://github.com/achekery/data-streaming/actions/workflows/python-app.yml/badge.svg)
-
-## 1. Design Summary
-For suffix pattern recognition with $K$ suffix patterns (length $W$) and 1 query pattern (length $N$), using **reverse-traversal prefix tree search** is efficient because it can model common ancestor ordering with reverse encoding (by inserting suffix patterns in reverse order during setup and searching in reverse order during queries) and check the multiple patterns over a single root-to-leaf pass (taking runtime $O(K\*W)$ for one-time setup and $O(W)$ for each query). This improves over using direct suffix pattern search which must check the multiple patterns over separate array passes (taking $O(K\*W)$ for each query) or using forward-traversal prefix tree search which cannot model common ancestor ordering and must check the multiple patterns over separate root-to-leaf passes (taking runtime $O(K\*W)$ for one-time setup and $O(K\*W)$ for each query).
-
-For batch data (offline scenario), reading the query pattern from a static array (size $N$) with a reverse iterator takes $O(1)$ auxiliary space. For streaming data (online scenario), reading the query pattern from a history array (size $W$) reconstructed from the stream takes $O(W)$ auxiliary space.
-
-### 📊 Complexity Analysis
-
-| Operation | Direct Search (v1) | Forward-traversal (v2) | Reverse-traversal (v3) | Comparison |
-| :--- | :--- | :--- | :--- | :--- |
-| **Initial Setup** | $O(1)$ | $O(K\*W)$ | $O(K\*W)$ | v1 is superior |
-| **Batch Queries (N)** | $O(K\*W)$ | $O(K\*W)$ | $O(W)$ | v3 is superior |
-| **Streaming Queries (1)** | $O(K\*W)$ | $O(K\*W)$ | $O(W)$ | v3 is superior |
-| **Space Complexity** | $O(1)$ | $O(K\*W)$ | $O(K\*W)$ | v1 is superior |
-
-### 🚀 Reverse Encoding (Visual)
-
-The advantage of reverse-traversal prefix tree search is that it can check multiple suffix patterns at once, ensuring $O(W)$ query time (and is independent of the suffix pattern count $K$ and the query pattern length $N$). This is possible because of reverse encoding.
-
-![Diagram for reverse encoding](static/diagram-image.png)
-
-## 2. Design Approaches & Trade-offs
-
-### When Less is More
-Although Direct Search (v1) requires ~90% less lines of code, it performs worse than Reverse-traversal (v3) in every comparison other than initial setup and space complexity. This trade-off shows that Direct Search may be preferable for low-memory systems that cannot afford higher space usage (like embedded systems) or greater maintenance scope (like regulated industries) and that Reverse-traversal may be preferable for systems with more resources (like compute nodes in distributed systems).
-
-### Python Object-Model Tuning
-To reduce object-overhead due to the Python object-model, I implemented a **nested hash map** for the reverse-traversal prefix tree, with each "node" using a character for the hash map key and a reference to the next "node" for the hash map value. This approach reduced object lookup during queries.
-
-## 3. API Reference
-
-::: data_streaming_accelerators.core.suffix_pattern_recognition
diff --git a/docs/suffix_pattern_recognition/README.md b/docs/modules/suffix_pattern_recognition/README.md
similarity index 97%
rename from docs/suffix_pattern_recognition/README.md
rename to docs/modules/suffix_pattern_recognition/README.md
index 3e87ae9..7a3d3a7 100644
--- a/docs/suffix_pattern_recognition/README.md
+++ b/docs/modules/suffix_pattern_recognition/README.md
@@ -19,7 +19,9 @@ For batch data (offline scenario), reading the query pattern from a static array
 
 The advantage of reverse-traversal prefix tree search is that it can check multiple suffix patterns at once, ensuring $O(W)$ query time (and is independent of the suffix pattern count $K$ and the query pattern length $N$). This is possible because of reverse encoding.
 
-![Diagram for reverse encoding](static/diagram-image.png)
+```mermaid
+{% include "modules/suffix_pattern_recognition/static/diagram-mermaid.txt" %}
+```
 
 ## 2. Design Approaches & Trade-offs
 
diff --git a/docs/suffix_pattern_recognition/static/diagram-image.png b/docs/modules/suffix_pattern_recognition/static/diagram-image.png
similarity index 100%
rename from docs/suffix_pattern_recognition/static/diagram-image.png
rename to docs/modules/suffix_pattern_recognition/static/diagram-image.png
diff --git a/docs/suffix_pattern_recognition/static/diagram-mermaid.txt b/docs/modules/suffix_pattern_recognition/static/diagram-mermaid.txt
similarity index 100%
rename from docs/suffix_pattern_recognition/static/diagram-mermaid.txt
rename to docs/modules/suffix_pattern_recognition/static/diagram-mermaid.txt
diff --git a/mkdocs.yml b/mkdocs.yml
index 01040e8..e571c8f 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -17,6 +17,8 @@ markdown_extensions:
 
 plugins:
   - search
+  - macros:
+      on_error_fail: true
   - mkdocstrings:
       handlers:
         python:
@@ -29,6 +31,6 @@ plugins:
 nav:
   - Overview: index.md
   - Modules:
-    - Dynamic Interval Management: modules/dynamic_interval_management.md
-    - Dynamic Point Aggregation: modules/dynamic_point_aggregation.md
-    - Suffix Pattern Recognition: modules/suffix_pattern_recognition.md
+    - Dynamic Interval Management: modules/dynamic_interval_management/README.md
+    - Dynamic Point Aggregation: modules/dynamic_point_aggregation/README.md
+    - Suffix Pattern Recognition: modules/suffix_pattern_recognition/README.md
diff --git a/pyproject.toml b/pyproject.toml
index e1bcda6..50b4a16 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -17,6 +17,7 @@ dev = [
     "pytest>=9.0.3",
 ]
 docs = [
+    "mkdocs-macros-plugin>=1.5.0",
     "mkdocs-material>=9.7.6",
     "mkdocs-mermaid2-plugin>=1.2.3",
     "mkdocstrings-python>=2.0.3",
diff --git a/uv.lock b/uv.lock
index df95116..e372fed 100644
--- a/uv.lock
+++ b/uv.lock
@@ -215,6 +215,7 @@ dev = [
     { name = "pytest" },
 ]
 docs = [
+    { name = "mkdocs-macros-plugin" },
     { name = "mkdocs-material" },
     { name = "mkdocs-mermaid2-plugin" },
     { name = "mkdocstrings", extra = ["python"] },
@@ -235,6 +236,7 @@ provides-extras = ["benchmark"]
 [package.metadata.requires-dev]
 dev = [{ name = "pytest", specifier = ">=9.0.3" }]
 docs = [
+    { name = "mkdocs-macros-plugin", specifier = ">=1.5.0" },
     { name = "mkdocs-material", specifier = ">=9.7.6" },
     { name = "mkdocs-mermaid2-plugin", specifier = ">=1.2.3" },
     { name = "mkdocstrings", extras = ["python"], specifier = ">=1.0.4" },
@@ -305,6 +307,15 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/11/8c/c9138d881c79aa0ea9ed83cbd58d5ca75624378b38cee225dcf5c42cc91f/griffelib-2.0.2-py3-none-any.whl", hash = "sha256:925c857658fb1ba40c0772c37acbc2ab650bd794d9c1b9726922e36ea4117ea1", size = 142357, upload-time = "2026-03-27T11:34:46.275Z" },
 ]
 
+[[package]]
+name = "hjson"
+version = "3.1.0"
+source = { registry = "https://pypi.org/simple" }
+sdist = { url = "https://files.pythonhosted.org/packages/82/e5/0b56d723a76ca67abadbf7fb71609fb0ea7e6926e94fcca6c65a85b36a0e/hjson-3.1.0.tar.gz", hash = "sha256:55af475a27cf83a7969c808399d7bccdec8fb836a07ddbd574587593b9cdcf75", size = 40541, upload-time = "2022-08-13T02:53:01.919Z" }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/1f/7f/13cd798d180af4bf4c0ceddeefba2b864a63c71645abc0308b768d67bb81/hjson-3.1.0-py3-none-any.whl", hash = "sha256:65713cdcf13214fb554eb8b4ef803419733f4f5e551047c9b711098ab7186b89", size = 54018, upload-time = "2022-08-13T02:52:59.899Z" },
+]
+
 [[package]]
 name = "idna"
 version = "3.14"
@@ -584,6 +595,27 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/88/29/744136411e785c4b0b744d5413e56555265939ab3a104c6a4b719dad33fd/mkdocs_get_deps-0.2.2-py3-none-any.whl", hash = "sha256:e7878cbeac04860b8b5e0ca31d3abad3df9411a75a32cde82f8e44b6c16ff650", size = 9555, upload-time = "2026-03-10T02:46:32.256Z" },
 ]
 
+[[package]]
+name = "mkdocs-macros-plugin"
+version = "1.5.0"
+source = { registry = "https://pypi.org/simple" }
+dependencies = [
+    { name = "hjson" },
+    { name = "jinja2" },
+    { name = "mkdocs" },
+    { name = "packaging" },
+    { name = "pathspec" },
+    { name = "python-dateutil" },
+    { name = "pyyaml" },
+    { name = "requests" },
+    { name = "super-collections" },
+    { name = "termcolor" },
+]
+sdist = { url = "https://files.pythonhosted.org/packages/92/15/e6a44839841ebc9c5872fa0e6fad1c3757424e4fe026093b68e9f386d136/mkdocs_macros_plugin-1.5.0.tar.gz", hash = "sha256:12aa45ce7ecb7a445c66b9f649f3dd05e9b92e8af6bc65e4acd91d26f878c01f", size = 37730, upload-time = "2025-11-13T08:08:55.545Z" }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/51/62/9fffba5bb9ed3d31a932ad35038ba9483d59850256ee0fea7f1187173983/mkdocs_macros_plugin-1.5.0-py3-none-any.whl", hash = "sha256:c10fabd812bf50f9170609d0ed518e54f1f0e12c334ac29141723a83c881dd6f", size = 44626, upload-time = "2025-11-13T08:08:53.878Z" },
+]
+
 [[package]]
 name = "mkdocs-material"
 version = "9.7.6"
@@ -1048,6 +1080,27 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/46/2c/1462b1d0a634697ae9e55b3cecdcb64788e8b7d63f54d923fcd0bb140aed/soupsieve-2.8.3-py3-none-any.whl", hash = "sha256:ed64f2ba4eebeab06cc4962affce381647455978ffc1e36bb79a545b91f45a95", size = 37016, upload-time = "2026-01-20T04:27:01.012Z" },
 ]
 
+[[package]]
+name = "super-collections"
+version = "0.6.2"
+source = { registry = "https://pypi.org/simple" }
+dependencies = [
+    { name = "hjson" },
+]
+sdist = { url = "https://files.pythonhosted.org/packages/e0/de/a0c3d1244912c260638f0f925e190e493ccea37ecaea9bbad7c14413b803/super_collections-0.6.2.tar.gz", hash = "sha256:0c8d8abacd9fad2c7c1c715f036c29f5db213f8cac65f24d45ecba12b4da187a", size = 31315, upload-time = "2025-09-30T00:37:08.067Z" }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/17/43/47c7cf84b3bd74a8631b02d47db356656bb8dff6f2e61a4c749963814d0d/super_collections-0.6.2-py3-none-any.whl", hash = "sha256:291b74d26299e9051d69ad9d89e61b07b6646f86a57a2f5ab3063d206eee9c56", size = 16173, upload-time = "2025-09-30T00:37:07.104Z" },
+]
+
+[[package]]
+name = "termcolor"
+version = "3.3.0"
+source = { registry = "https://pypi.org/simple" }
+sdist = { url = "https://files.pythonhosted.org/packages/46/79/cf31d7a93a8fdc6aa0fbb665be84426a8c5a557d9240b6239e9e11e35fc5/termcolor-3.3.0.tar.gz", hash = "sha256:348871ca648ec6a9a983a13ab626c0acce02f515b9e1983332b17af7979521c5", size = 14434, upload-time = "2025-12-29T12:55:21.882Z" }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/33/d1/8bb87d21e9aeb323cc03034f5eaf2c8f69841e40e4853c2627edf8111ed3/termcolor-3.3.0-py3-none-any.whl", hash = "sha256:cf642efadaf0a8ebbbf4bc7a31cec2f9b5f21a9f726f4ccbb08192c9c26f43a5", size = 7734, upload-time = "2025-12-29T12:55:20.718Z" },
+]
+
 [[package]]
 name = "typing-extensions"
 version = "4.15.0"

From f5082b277724b418f5ad4779f80825a793aae13e Mon Sep 17 00:00:00 2001
From: achekery <6503526+achekery@users.noreply.github.com>
Date: Tue, 12 May 2026 22:21:50 -0700
Subject: [PATCH 07/12] fix indent for docs.yml

---
 .github/workflows/docs.yml | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml
index 13adc64..9f80c8f 100644
--- a/.github/workflows/docs.yml
+++ b/.github/workflows/docs.yml
@@ -8,16 +8,16 @@ jobs:
     runs-on: ubuntu-latest
 
     steps:
-      - uses: actions/checkout@v6
+    - uses: actions/checkout@v6
 
-      - name: Setup python
-        uses: actions/setup-python@v6
-        with:
-          python-version-file: "pyproject.toml"
+    - name: Setup python
+      uses: actions/setup-python@v6
+      with:
+        python-version-file: "pyproject.toml"
 
-      - name: Setup uv
-        uses: astral-sh/setup-uv@08807647e7069bb48b6ef5acd8ec9567f424441b # v8.1.0
+    - name: Setup uv
+      uses: astral-sh/setup-uv@08807647e7069bb48b6ef5acd8ec9567f424441b # v8.1.0
 
-      - name: Build docs with mkdocs
-        run: |
-          uv run --group docs mkdocs gh-deploy -v --clean --strict --force
+    - name: Build docs with mkdocs
+      run: |
+        uv run --group docs mkdocs gh-deploy -v --clean --strict --force

From 491801ee424c89a938668ea27c4e6a6416556d83 Mon Sep 17 00:00:00 2001
From: achekery <6503526+achekery@users.noreply.github.com>
Date: Wed, 13 May 2026 11:11:29 -0700
Subject: [PATCH 08/12] fix latex rendering with mathjax

---
 .github/workflows/python-app.yml               |   2 +-
 DEVELOPMENT.md                                 |  12 ------------
 docs/javascripts/mathjax.js                    |  16 ++++++++++++++++
 .../static/pruning-diagram.png                 | Bin 223372 -> 0 bytes
 .../suffix_pattern_recognition/README.md       |  10 +++++-----
 .../static/diagram-image.png                   | Bin 244294 -> 0 bytes
 mkdocs.yml                                     |   4 ++++
 7 files changed, 26 insertions(+), 18 deletions(-)
 create mode 100644 docs/javascripts/mathjax.js
 delete mode 100644 docs/modules/dynamic_interval_management/static/pruning-diagram.png
 delete mode 100644 docs/modules/suffix_pattern_recognition/static/diagram-image.png

diff --git a/.github/workflows/python-app.yml b/.github/workflows/python-app.yml
index f90c226..3a2547e 100644
--- a/.github/workflows/python-app.yml
+++ b/.github/workflows/python-app.yml
@@ -28,7 +28,7 @@ jobs:
       run: |
         uv run --group dev --extra benchmark pytest -sv
 
-    - name: Upload artifacts from package tests
+    - name: Upload artifacts from tests
       uses: actions/upload-artifact@v4
       with:
         name: artifacts
diff --git a/DEVELOPMENT.md b/DEVELOPMENT.md
index 161444a..92902cc 100644
--- a/DEVELOPMENT.md
+++ b/DEVELOPMENT.md
@@ -4,18 +4,6 @@ TODO: Verify gh-deploy workflow is successful
 
 TODO: Verify mkdocs generation is successful
 
-```
-uv run mkdocs serve -v
-```
-
-TODO: Remove unnecessary files
-
-```
-rm -rf docs/dynamic_interval_management/
-rm -rf docs/dynamic_point_aggregation/
-rm -rf docs/suffix_pattern_recognition/
-```
-
 ## Run tests with pytest
 
 ```sh
diff --git a/docs/javascripts/mathjax.js b/docs/javascripts/mathjax.js
new file mode 100644
index 0000000..ec9a9a3
--- /dev/null
+++ b/docs/javascripts/mathjax.js
@@ -0,0 +1,16 @@
+window.MathJax = {
+  tex: {
+    inlineMath: [["\\(", "\\)"]],
+    displayMath: [["\\[", "\\]"]],
+    processEscapes: true,
+    processEnvironments: true
+  },
+  options: {
+    ignoreHtmlClass: ".*|",
+    processHtmlClass: "arithmatex"
+  }
+};
+
+document.subscribe(() => { 
+  MathJax.typesetPromise()
+})
\ No newline at end of file
diff --git a/docs/modules/dynamic_interval_management/static/pruning-diagram.png b/docs/modules/dynamic_interval_management/static/pruning-diagram.png
deleted file mode 100644
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GIT binary patch
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diff --git a/docs/modules/suffix_pattern_recognition/README.md b/docs/modules/suffix_pattern_recognition/README.md
index 7a3d3a7..b4086fe 100644
--- a/docs/modules/suffix_pattern_recognition/README.md
+++ b/docs/modules/suffix_pattern_recognition/README.md
@@ -2,7 +2,7 @@
 ![Python CI](https://github.com/achekery/data-streaming/actions/workflows/python-app.yml/badge.svg)
 
 ## 1. Design Summary
-For suffix pattern recognition with $K$ suffix patterns (length $W$) and 1 query pattern (length $N$), using **reverse-traversal prefix tree search** is efficient because it can model common ancestor ordering with reverse encoding (by inserting suffix patterns in reverse order during setup and searching in reverse order during queries) and check the multiple patterns over a single root-to-leaf pass (taking runtime $O(K\*W)$ for one-time setup and $O(W)$ for each query). This improves over using direct suffix pattern search which must check the multiple patterns over separate array passes (taking $O(K\*W)$ for each query) or using forward-traversal prefix tree search which cannot model common ancestor ordering and must check the multiple patterns over separate root-to-leaf passes (taking runtime $O(K\*W)$ for one-time setup and $O(K\*W)$ for each query).
+For suffix pattern recognition with $K$ suffix patterns (length $W$) and 1 query pattern (length $N$), using **reverse-traversal prefix tree search** is efficient because it can model common ancestor ordering with reverse encoding (by inserting suffix patterns in reverse order during setup and searching in reverse order during queries) and check the multiple patterns over a single root-to-leaf pass (taking runtime $O(K \cdot W)$ for one-time setup and $O(W)$ for each query). This improves over using direct suffix pattern search which must check the multiple patterns over separate array passes (taking $O(K \cdot W)$ for each query) or using forward-traversal prefix tree search which cannot model common ancestor ordering and must check the multiple patterns over separate root-to-leaf passes (taking runtime $O(K \cdot W)$ for one-time setup and $O(K \cdot W)$ for each query).
 
 For batch data (offline scenario), reading the query pattern from a static array (size $N$) with a reverse iterator takes $O(1)$ auxiliary space. For streaming data (online scenario), reading the query pattern from a history array (size $W$) reconstructed from the stream takes $O(W)$ auxiliary space.
 
@@ -10,10 +10,10 @@ For batch data (offline scenario), reading the query pattern from a static array
 
 | Operation | Direct Search (v1) | Forward-traversal (v2) | Reverse-traversal (v3) | Comparison |
 | :--- | :--- | :--- | :--- | :--- |
-| **Initial Setup** | $O(1)$ | $O(K\*W)$ | $O(K\*W)$ | v1 is superior |
-| **Batch Queries (N)** | $O(K\*W)$ | $O(K\*W)$ | $O(W)$ | v3 is superior |
-| **Streaming Queries (1)** | $O(K\*W)$ | $O(K\*W)$ | $O(W)$ | v3 is superior |
-| **Space Complexity** | $O(1)$ | $O(K\*W)$ | $O(K\*W)$ | v1 is superior |
+| **Initial Setup** | $O(1)$ | $O(K \cdot W)$ | $O(K \cdot W)$ | v1 is superior |
+| **Batch Queries (N)** | $O(K \cdot W)$ | $O(K \cdot W)$ | $O(W)$ | v3 is superior |
+| **Streaming Queries (1)** | $O(K \cdot W)$ | $O(K \cdot W)$ | $O(W)$ | v3 is superior |
+| **Space Complexity** | $O(1)$ | $O(K \cdot W)$ | $O(K \cdot W)$ | v1 is superior |
 
 ### 🚀 Reverse Encoding (Visual)
 
diff --git a/docs/modules/suffix_pattern_recognition/static/diagram-image.png b/docs/modules/suffix_pattern_recognition/static/diagram-image.png
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diff --git a/mkdocs.yml b/mkdocs.yml
index e571c8f..fee12f0 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -34,3 +34,7 @@ nav:
     - Dynamic Interval Management: modules/dynamic_interval_management/README.md
     - Dynamic Point Aggregation: modules/dynamic_point_aggregation/README.md
     - Suffix Pattern Recognition: modules/suffix_pattern_recognition/README.md
+
+extra_javascript:
+  - javascripts/mathjax.js
+  - https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js

From cb7dece626a6c8e0d6b6c942b645730a863a5e53 Mon Sep 17 00:00:00 2001
From: achekery <6503526+achekery@users.noreply.github.com>
Date: Wed, 13 May 2026 11:14:27 -0700
Subject: [PATCH 09/12] fix latex rendering with mathjax

---
 docs/javascripts/mathjax.js                        | 2 +-
 docs/modules/dynamic_interval_management/README.md | 4 +---
 2 files changed, 2 insertions(+), 4 deletions(-)

diff --git a/docs/javascripts/mathjax.js b/docs/javascripts/mathjax.js
index ec9a9a3..b186af6 100644
--- a/docs/javascripts/mathjax.js
+++ b/docs/javascripts/mathjax.js
@@ -13,4 +13,4 @@ window.MathJax = {
 
 document.subscribe(() => { 
   MathJax.typesetPromise()
-})
\ No newline at end of file
+})
diff --git a/docs/modules/dynamic_interval_management/README.md b/docs/modules/dynamic_interval_management/README.md
index 680b648..404965f 100644
--- a/docs/modules/dynamic_interval_management/README.md
+++ b/docs/modules/dynamic_interval_management/README.md
@@ -69,9 +69,7 @@ To ensure system reliability during high-frequency updates, I prioritized **Corr
 By implementing a **Sentinel Node Architecture** with a **Two-Down** AVL balancing subtree rotation strategy and removing the need for sentinel node checks throughout the codebase, I simplified the balancing feature and provided a cleaner and more maintainable implementation.
 
 ### Python Object-Model Tuning
-To reduce object-overhead due to the Python object-model, I implemented **Attribute Flattening**. After replacing packed collections (`self.interval[0]`) with discrete integers (`self.lo`, `self.hi`), I reduced constant factors in the hot execution path and achieved a **15% reduction** in benchmarks with static intervals. 123
-
-test
+To reduce object-overhead due to the Python object-model, I implemented **Attribute Flattening**. After replacing packed collections (`self.interval[0]`) with discrete integers (`self.lo`, `self.hi`), I reduced constant factors in the hot execution path and achieved a **15% reduction** in benchmarks with static intervals.
 
 ## 5. Getting Started
 

From 9062f28cf297cd6da5c0dcb524f6950b71f091d6 Mon Sep 17 00:00:00 2001
From: achekery <6503526+achekery@users.noreply.github.com>
Date: Wed, 13 May 2026 11:32:14 -0700
Subject: [PATCH 10/12] add repo information

---
 DEVELOPMENT.md | 2 --
 mkdocs.yml     | 6 ++++++
 2 files changed, 6 insertions(+), 2 deletions(-)

diff --git a/DEVELOPMENT.md b/DEVELOPMENT.md
index 92902cc..dff7c0e 100644
--- a/DEVELOPMENT.md
+++ b/DEVELOPMENT.md
@@ -2,8 +2,6 @@
 
 TODO: Verify gh-deploy workflow is successful
 
-TODO: Verify mkdocs generation is successful
-
 ## Run tests with pytest
 
 ```sh
diff --git a/mkdocs.yml b/mkdocs.yml
index fee12f0..133d62e 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -1,5 +1,11 @@
 site_name: Data Streaming Accelerators
+site_url: https://achekery.github.io/data-streaming-accelerators/
+
+repo_name: Data Streaming Accelerators
+repo_url: https://github.com/achekery/data-streaming-accelerators/
+
 theme:
+  language: en
   name: material
   features:
     - content.code.copy

From d964ce7a82885cfbbb24570f320e0c0ed5f0605b Mon Sep 17 00:00:00 2001
From: achekery <6503526+achekery@users.noreply.github.com>
Date: Wed, 13 May 2026 12:06:58 -0700
Subject: [PATCH 11/12] finalize mkdocs build

---
 DEVELOPMENT.md                                     |  2 --
 docs/index.md                                      | 14 +++++++++++++-
 docs/modules/dynamic_interval_management/README.md |  6 ++++--
 docs/modules/dynamic_point_aggregation/README.md   |  2 ++
 docs/modules/suffix_pattern_recognition/README.md  |  2 ++
 mkdocs.yml                                         |  2 ++
 6 files changed, 23 insertions(+), 5 deletions(-)

diff --git a/DEVELOPMENT.md b/DEVELOPMENT.md
index dff7c0e..22cf20a 100644
--- a/DEVELOPMENT.md
+++ b/DEVELOPMENT.md
@@ -1,7 +1,5 @@
 # DEVELOPMENT
 
-TODO: Verify gh-deploy workflow is successful
-
 ## Run tests with pytest
 
 ```sh
diff --git a/docs/index.md b/docs/index.md
index 5e733fd..78d4b94 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -2,4 +2,16 @@
 
 ![Python CI](https://github.com/achekery/data-streaming/actions/workflows/python-app.yml/badge.svg)
 
-TODO: Add a high-level summary of the whole suite
+## [Dynamic Interval Management](modules/dynamic_interval_management)
+
+--8<-- "modules/dynamic_interval_management/README.md:summary"
+
+![Graph for Performance Report](modules/dynamic_interval_management/static/performance-report-1280x640.png)
+
+## Dynamic Point Aggregation
+
+--8<-- "modules/dynamic_point_aggregation/README.md:summary"
+
+## Suffix Pattern Recognition
+
+--8<-- "modules/suffix_pattern_recognition/README.md:summary"
diff --git a/docs/modules/dynamic_interval_management/README.md b/docs/modules/dynamic_interval_management/README.md
index 404965f..f983df6 100644
--- a/docs/modules/dynamic_interval_management/README.md
+++ b/docs/modules/dynamic_interval_management/README.md
@@ -2,7 +2,11 @@
 ![Python CI](https://github.com/achekery/data-streaming/actions/workflows/python-app.yml/badge.svg)
 
 ## 1. Design Summary
+<!-- --8<-- [start:summary] -->
 The theoretical lower bound for merging $N$ static intervals is $\Omega(N \log N)$ due to the sorting requirement. By focusing on interval edges rather than the source intervals themselves, we can focus on efficient algorithms with compact implementation.  However, in **Online Streaming Environments**, the task shifts from batch data loading (static intervals) to streaming data ingestion (dynamic intervals).
+<!-- --8<-- [end:summary] -->
+
+![Graph for Performance Report](static/performance-report-1280x640.png)
 
 ### 📊 Complexity Analysis
 
@@ -55,8 +59,6 @@ In benchmarks with dynamic intervals up to $N=3000$, the Interval Tree (Variant
 | 2000 | 0.6743 | 0.0383 | 17.6x |
 | 3000 | 1.6093 | 0.0318 | **50.6x** |
 
-![Graph for Performance Report](static/performance-report-1280x640.png)
-
 ## 4. Design Optimizations
 
 ### Augmented Metadata
diff --git a/docs/modules/dynamic_point_aggregation/README.md b/docs/modules/dynamic_point_aggregation/README.md
index 89563e8..0c04b8d 100644
--- a/docs/modules/dynamic_point_aggregation/README.md
+++ b/docs/modules/dynamic_point_aggregation/README.md
@@ -2,11 +2,13 @@
 ![Python CI](https://github.com/achekery/data-streaming/actions/workflows/python-app.yml/badge.svg)
 
 ## 1. Design Summary
+<!-- --8<-- [start:summary] -->
 The optimal runtime complexity for dynamic point aggregation from $N$ point values to $O(N)$ disjoint intervals is $\Omega(N \log N)$ due to the ordering requirement. The request handler uses `put` requests to add new values and `get` requests to make a new interval sequence.
 
 Because offline scenarios (batch data) have known usage patterns, the batch variant (V1) can **optimize the hot path** by simplifying high-usage `put` requests to $O(1)$ and expanding low-usage `get` requests to $O(N \log N)$.
 
 However, because online scenarios (streaming data) do not have known usage patterns, the streaming variant (V2) must instead **balance complexity** between `put` requests ($O(\log N)$) and `get` requests ($O(N)$).
+<!-- --8<-- [end:summary] -->
 
 ### 📊 Complexity Analysis
 
diff --git a/docs/modules/suffix_pattern_recognition/README.md b/docs/modules/suffix_pattern_recognition/README.md
index b4086fe..3625c7e 100644
--- a/docs/modules/suffix_pattern_recognition/README.md
+++ b/docs/modules/suffix_pattern_recognition/README.md
@@ -2,9 +2,11 @@
 ![Python CI](https://github.com/achekery/data-streaming/actions/workflows/python-app.yml/badge.svg)
 
 ## 1. Design Summary
+<!-- --8<-- [start:summary] -->
 For suffix pattern recognition with $K$ suffix patterns (length $W$) and 1 query pattern (length $N$), using **reverse-traversal prefix tree search** is efficient because it can model common ancestor ordering with reverse encoding (by inserting suffix patterns in reverse order during setup and searching in reverse order during queries) and check the multiple patterns over a single root-to-leaf pass (taking runtime $O(K \cdot W)$ for one-time setup and $O(W)$ for each query). This improves over using direct suffix pattern search which must check the multiple patterns over separate array passes (taking $O(K \cdot W)$ for each query) or using forward-traversal prefix tree search which cannot model common ancestor ordering and must check the multiple patterns over separate root-to-leaf passes (taking runtime $O(K \cdot W)$ for one-time setup and $O(K \cdot W)$ for each query).
 
 For batch data (offline scenario), reading the query pattern from a static array (size $N$) with a reverse iterator takes $O(1)$ auxiliary space. For streaming data (online scenario), reading the query pattern from a history array (size $W$) reconstructed from the stream takes $O(W)$ auxiliary space.
+<!-- --8<-- [end:summary] -->
 
 ### 📊 Complexity Analysis
 
diff --git a/mkdocs.yml b/mkdocs.yml
index 133d62e..2d4243d 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -20,6 +20,8 @@ markdown_extensions:
           format: !!python/name:pymdownx.superfences.fence_code_format
   - pymdownx.arithmatex:
       generic: true # For your O(log N) LaTeX notations
+  - pymdownx.snippets:
+      base_path: docs
 
 plugins:
   - search

From efae4d6f9cb13ba2a13dfa655c7af68c2c3a244a Mon Sep 17 00:00:00 2001
From: achekery <6503526+achekery@users.noreply.github.com>
Date: Wed, 13 May 2026 12:16:54 -0700
Subject: [PATCH 12/12] finalize mkdocs build

---
 docs/index.md                                 | 19 ++++++++++++++++---
 .../dynamic_interval_management/README.md     | 11 +----------
 2 files changed, 17 insertions(+), 13 deletions(-)

diff --git a/docs/index.md b/docs/index.md
index 78d4b94..7b64255 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -2,16 +2,29 @@
 
 ![Python CI](https://github.com/achekery/data-streaming/actions/workflows/python-app.yml/badge.svg)
 
-## [Dynamic Interval Management](modules/dynamic_interval_management)
+## 1. Summary
+
+### [Dynamic Interval Management](modules/dynamic_interval_management)
 
 --8<-- "modules/dynamic_interval_management/README.md:summary"
 
 ![Graph for Performance Report](modules/dynamic_interval_management/static/performance-report-1280x640.png)
 
-## Dynamic Point Aggregation
+### Dynamic Point Aggregation
 
 --8<-- "modules/dynamic_point_aggregation/README.md:summary"
 
-## Suffix Pattern Recognition
+### Suffix Pattern Recognition
 
 --8<-- "modules/suffix_pattern_recognition/README.md:summary"
+
+
+## 2. Getting Started
+
+This design requires **Python 3.13+**.
+
+To run the regression tests for this design:
+
+```bash
+uv run --group dev --extra benchmark pytest -sv
+```
diff --git a/docs/modules/dynamic_interval_management/README.md b/docs/modules/dynamic_interval_management/README.md
index f983df6..21111fc 100644
--- a/docs/modules/dynamic_interval_management/README.md
+++ b/docs/modules/dynamic_interval_management/README.md
@@ -73,15 +73,6 @@ By implementing a **Sentinel Node Architecture** with a **Two-Down** AVL balanci
 ### Python Object-Model Tuning
 To reduce object-overhead due to the Python object-model, I implemented **Attribute Flattening**. After replacing packed collections (`self.interval[0]`) with discrete integers (`self.lo`, `self.hi`), I reduced constant factors in the hot execution path and achieved a **15% reduction** in benchmarks with static intervals.
 
-## 5. Getting Started
-
-This design requires **Python 3.13+**.
-
-To run the regression tests for this design:
-```bash
-uv run --group dev --extra benchmark pytest -sv
-```
-
-## 6. API Reference
+## 5. API Reference
 
 ::: data_streaming_accelerators.core.dynamic_interval_management