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The Complexity of Boolean Matrix Root Computation

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Computing and Combinatorics (COCOON 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2697))

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Abstract

We show that finding roots of Boolean matrices is an NPhard problem. This answers a twenty year old question from semigroup theory. Interpreting Boolean matrices as directed graphs, we further reveal a connection between Boolean matrix roots and graph isomorphism, which leads to a proof that for a certain subclass of Boolean matrices related to subdivision digraphs, root finding is of the same complexity as the graph-isomorphism problem.

Member of the European graduate school “Combinatorics, Geometry, and Computation” supported by the Deutsche Forschungsgemeinschaft, grant GRK 588/2.

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Author information

Authors and Affiliations

  1. Freie Universität Berlin, Germany

    Martin Kutz

Authors
  1. Martin Kutz
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at Austin, One University Station, C0500, Austin, TX, 78712, USA

    Tandy Warnow

  2. Department of Computer Science, Montana State University, EPS 357, Bozeman, MT, 59717, USA

    Binhai Zhu

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© 2003 Springer-Verlag Berlin Heidelberg

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Kutz, M. (2003). The Complexity of Boolean Matrix Root Computation. In: Warnow, T., Zhu, B. (eds) Computing and Combinatorics. COCOON 2003. Lecture Notes in Computer Science, vol 2697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45071-8_23

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  • DOI: https://doi.org/10.1007/3-540-45071-8_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40534-4

  • Online ISBN: 978-3-540-45071-9

  • eBook Packages: Springer Book Archive

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