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Implement strategy for loop ordering choice (true compiler starter) #51651

@aartbik

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@aartbik
Bugzilla Link 52309
Version unspecified
OS Linux
CC @joker-eph

Extended Description

The sparse compiler uses a topsort to find a suitable loop ordering (following the sparse constraints always, and possibly adding in the dense constraints if this does not yield cycles). However, often we still have an ordering choice, and the way we currently go from conservative ordering to relaxed ordering can possibly be improved. The bug requests investigating and implementing a good strategy for picking a loop order.

Relevant code to start looking at:

Method computeIterationGraph() in https://github.com/llvm/llvm-project/blob/main/mlir/lib/Dialect/SparseTensor/Transforms/Sparsification.cpp

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bugzillaIssues migrated from bugzillagood first issuehttps://github.com/llvm/llvm-project/contributemlir:tensor

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