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A potential optimization is to loop over n, where n is rows with non-zero values. |
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Good suggestion. I added an optimization where we only iterate over vertices that have nonempty rows and nonempty columns. I think this behaves correctly, but would appreciate if somebody could verify it. I also introduced another temporary matrix to hold the outer product. We then drop the diagonal values from them. All this performs better or similar in my limited benchmarking. Our strategy of keeping things sparse is probably reasonable, because what if there are multiple groups of connected components? The final result frequently may not be dense. With the goal of "keeping things sparse", I wonder if there are any heuristics we could employ, such as iterating over vertices with small degrees first. |
| A, row_degrees, column_degrees = G.get_properties("offdiag row_degrees- column_degrees-") | ||
| nonempty_nodes = binary.pair(row_degrees & column_degrees).new(name="nonempty_nodes") | ||
| else: | ||
| A, nonempty_nodes = G.get_properties("offdiag degrees-") |
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Note that we use some shorthand notation here. "degrees-" does not include self-edges (i.e., diagonals), but "degrees+" does include self-edges.
| Row = Matrix(dtype, nrows=1, ncols=n, name="Row") | ||
| Col = Matrix(dtype, nrows=n, ncols=1, name="Col") | ||
| Outer = Matrix(dtype, nrows=n, ncols=n, name="temp") | ||
| for i in nonempty_nodes: |
Not sure about this, it could lead to gotchas if users don't expect sorting to happen. (and sorting itself could be an issue, e.g. when using distributed graphs) |
CC @jim22k @SultanOrazbayev @LuisFelipeRamos
I made a few minor modifications to the algorithms from what we wrote together today. I'm happy to answer any questions. I tinkered around a little to make things faster.
We can probably get this to work with
dask-graphblastoo, which I think would be pretty interesting, because it can create a massive, distributed matrix. It may not be the best way to compute APSP, but a way is better than no way at all :)See the original LAGraph version of Floyd-Warshall here:
https://github.com/GraphBLAS/LAGraph/blob/ed55a49ee7138d2b5a6c5eb4329ccd0bf9e4ac17/old/experimental_algorithm/LAGraph_FW.c
I'll try to benchmark and compare this with a NumPy implementation on a beefy machine with lots of memory.