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    A fast search algorithm for (m,m,m) triple product property triples and an application for 5 × 5 matrix multiplication

    Hart, Sarah B. and Hedtke, I. and Mueller-Hannemann, M. and Murthy, S. (2015) A fast search algorithm for (m,m,m) triple product property triples and an application for 5 × 5 matrix multiplication. Groups Complexity Cryptology 7 (1), pp. 31-46. ISSN 1869-6104.

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    Abstract

    We present a new fast search algorithm for (m,m,m) Triple Product Property (TPP) triples as defined by Cohn and Umans in 2003. The new algorithm achieves a speed-up factor of 40 up to 194 in comparison to the best known search algorithm. With a parallelized version of the new algorithm we are able to search for TPP triples in groups up to order 55. As an application we identify a list “C1” of groups that could realize 5×5 matrix multiplication with under 100 resp. 125 scalar multiplications (the best known upper bound by Makarov 1987 resp. the trivial upper bound) if they contain a (5,5,5) TPP triple. With our new algorithm we show that no group in this list can realize 5×5 matrix multiplication better than Makarov’s algorithm. We also show a direction to modified group-theoretic search, not covered by C1 list.

    Metadata

    Item Type: Article
    Keyword(s) / Subject(s): Fast matrix multiplication, search algorithm, triple product property, group algebra rank
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Sarah Hart
    Date Deposited: 27 Apr 2015 06:50
    Last Modified: 03 Apr 2019 09:51
    URI: http://eprints.bbk.ac.uk/id/eprint/11416

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