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Bulk-synchronous parallel multiplication of boolean matrices

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Automata, Languages and Programming (ICALP 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1443))

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Abstract

The model of bulk-synchronous parallel (BSP) computation is an emerging paradigm of general-purpose parallel computing. We study the BSP complexity of subcubic algorithms for Boolean matrix multiplication. The communication cost of a standard Strassen-type algorithm is known to be optimal for general matrices. A natural question is whether it remains optimal when the problem is restricted to Boolean matrices. We give a negative answer to this question, by showing how to achieve a lower asymptotic communication cost for Boolean matrix multiplication. The proof uses a deep result from extremal graph theory, known as Szemerédi's Regularity Lemma. Despite its theoretical interest, the algorithm is not practical, because it works only on astronomically large matrices and involves huge constant factors.

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Kim G. Larsen Sven Skyum Glynn Winskel

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© 1998 Springer-Verlag Berlin Heidelberg

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Tiskin, A. (1998). Bulk-synchronous parallel multiplication of boolean matrices. In: Larsen, K.G., Skyum, S., Winskel, G. (eds) Automata, Languages and Programming. ICALP 1998. Lecture Notes in Computer Science, vol 1443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055078

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  • DOI: https://doi.org/10.1007/BFb0055078

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64781-2

  • Online ISBN: 978-3-540-68681-1

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