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 \(n^3\).
H. Yu—Supported in part by NSF CCF-1212372.
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Yu, H. (2015). An Improved Combinatorial Algorithm for Boolean Matrix Multiplication. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47672-7_89
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DOI: https://doi.org/10.1007/978-3-662-47672-7_89
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