An improved combinatorial algorithm for Boolean matrix multiplication
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A new combinatorial algorithm for triangle finding and Boolean matrix multiplication that runs in O ˆ ( n 3 / log 4 n ) time, where the O £ notation suppresses poly(loglog) factors.Abstract:
We present a new combinatorial algorithm for triangle finding and Boolean matrix multiplication that runs in O ˆ ( n 3 / log 4 n ) time, where the O ˆ notation suppresses poly(loglog) factors. This improves the previous best combinatorial algorithm by Chan that runs in O ˆ ( 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 .read more
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