Subcubic Equivalence of Triangle Detection and Matrix Multiplication
نویسندگان
چکیده
• The all-pairs shortest paths problem on weighted digraphs (APSP). • Detecting if a weighted graph has a triangle of negative total edge weight. • Listing up to n2.99 negative triangles in an edge-weighted graph. • Finding a minimum weight cycle in a graph of non-negative edge weights. • The replacement paths problem on weighted digraphs. • Finding the second shortest simple path between two nodes in a weighted digraph. • Checking whether a given matrix de?nes a metric. • Verifying the correctness of a matrix product over the (min, +)-semiring.
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