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Thin matrix products up to D <= N^0.172 and lossless reductions for 3SUM, Exact Triangle and APSP, with 3SUM over abelian groups and a dichotomy for coordinatewise problems
Alman and Vassilevska Williams (arXiv:2610.06783) gave the first polynomial improvements over the textbook algorithms for 3SUM and APSP: deterministic algorithms with exponents 1.9992 for 3SUM, 2.9983 for Exact Triangle and 2.99942 for APSP. Their algorithm has two steps: a matrix theorem, computing
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