An Improved Combinatorial Algorithm for Boolean Matrix Multiplication

Abstract

We present a new combinatorial algorithm for triangle finding and Boolean matrix multiplication that runs in $\hat{O}(n^3/{\log }^{4}n)$ time, where the $\hat{O}$ notation suppresses poly(loglog) factors. This improves the previous best combinatorial algorithm by Chan that runs in $\hat{O}(n^3/{\log }^{3}n)$ time. Our algorithm generalizes the divide-and-conquer strategy of Chan's algorithm. Moreover, we propose a general framework for detecting triangles in graphs and computing Boolean matrix multiplication. Roughly speaking, if we can find the "easy parts" of a given instance efficiently, we can solve the whole problem faster than $n^3$.

A preliminary version of this paper appeared in ICALP 2015

References in corpus (1)

• Powers of Tensors and Fast Matrix Multiplication