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We say an algorithm on n × n matrices with entries in [-M, M] (or n-node graphs with edge weights from [-M, M]) is truly subcubic if it runs in O(n3-δ - poly(log M)) time for some δ > 0. We define a notion of subcubic reducibility, and show that many important problems on graphs and matrices solvable in O(n3) time are equivalent under subcubic reductions. Namely, the following weighted problems...
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