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Hardness Results for Tournament Isomorphism and Automorphism

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Mathematical Foundations of Computer Science 2007 (MFCS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4708))

Abstract

A tournament is a graph in which each pair of distinct vertices is connected by exactly one directed edge. Tournaments are an important graph class, for which isomorphism testing seems to be easier to compute than for the isomorphism problem of general graphs. We show that tournament isomorphism and tournament automorphism is hard under DLOGTIME uniform AC0 many-one reductions for the complexity classes NL, C=L, PL (probabilistic logarithmic space), for logarithmic space modular counting classes Mod kL with odd k ≥ 3 and for DET, the class of problems, NC1 reducible to the determinant. These lower bounds have been proven for graph isomorphism, see [21].

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  1. Institut für Theoretische Informatik, Universität Ulm, 89073 Ulm, Germany

    Fabian Wagner

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  1. Fabian Wagner
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Luděk Kučera Antonín Kučera

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Wagner, F. (2007). Hardness Results for Tournament Isomorphism and Automorphism. In: Kučera, L., Kučera, A. (eds) Mathematical Foundations of Computer Science 2007. MFCS 2007. Lecture Notes in Computer Science, vol 4708. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74456-6_51

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  • DOI: https://doi.org/10.1007/978-3-540-74456-6_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74455-9

  • Online ISBN: 978-3-540-74456-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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