An Improved Combinatorial Algorithm for Boolean Matrix Multiplication
نویسنده
چکیده
We present a new combinatorial algorithm for triangle finding and Boolean matrix multiplication that runs in Ô(n/ log n) time, where the Ô notation suppresses poly(loglog) factors. This improves the previous best combinatorial algorithm by Chan [4] that runs in Ô(n/ log 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.
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