Subquadratic 3SUM and Subcubic APSP

Automated excerpt

Abstract:We give the first polynomial improvements over the textbook algorithms for $3$SUM and All-Pairs Shortest Paths (APSP): we show how to deterministically solve $3$SUM on $n$ integers of polynomial size in $O(n^{1. 9992})$ time and APSP on directed $n$-vertex graphs with polynomially bounded integer weights in $O(n^{2. 9995})$ time. This refutes the $3$SUM and APSP hypotheses. By known reductions, Exact Triangle, and hence $3$SUM and APSP, reduce to this problem.

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