Improve exhaustive dense subgraph finder for recursive assembly#103
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Improve exhaustive dense subgraph finder for recursive assembly#103
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The old routine does a depth-first search, which doesn't actually find *minimum* dense subgraphs, which a a breadth-first search does find. Finding small dense subgraphs is important for solving performance. Note both the DFS and the BFS implementations have exponential time-complexity, but BFS will in general lead to constructing more efficient decomposition plans. #97 introduced a polynomial-time *minimal* dense subgraph finder (not *minimum*). Its correctness is harder to check, so I'm thinking to keep the exhaustive search too, for now, mainly for ease of debugging. In addition to changing to BFS, this now makes use of the sparsity of the graph (normally, most elements only have a few incident edges) to reduce the amount of scanning performed, making this more useful in practice.
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waywardmonkeys
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The old routine does a depth-first search, which doesn't actually find minimum dense subgraphs, which a a breadth-first search does find. Finding small dense subgraphs is important for solving performance. Note both the DFS and the BFS implementations have exponential time-complexity, but BFS will in general lead to constructing more efficient decomposition plans.
#97 introduced a polynomial-time minimal dense subgraph finder (not minimum). Its correctness is harder to check, so I'm thinking to keep the exhaustive search too, for now, mainly for ease of debugging.
In addition to changing to BFS, this now makes use of the sparsity of the graph (normally, most elements only have a few incident edges) to reduce the amount of scanning performed, making this more useful in practice.