ICALP 2015: Automata, Languages, and Programming pp 1094-1105

# An Improved Combinatorial Algorithm for Boolean Matrix Multiplication

• Huacheng Yu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9134)

## 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 [4] 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 $$n^3$$.

## Keywords

Recursive Call Combinatorial Algorithm Left Child Recursion Tree Regularity Lemma
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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