We present a new combinatorial algorithm for triangle finding and Boolean matrix multiplication that runs in O(n 3 / log 4 n) time, where theÔ notation suppresses poly(loglog) factors. This improves the previous best combinatorial algorithm by Chan [4] that runs inÔ(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 .
Currently, the fastest such algorithm runs asymptotically in timê O(n 3 /log 4 n) REF .
An Improved Combinatorial Algorithm for Boolean Matrix Multiplication
ArXiv
ArXiv
Mathematics Computer Science