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The Computational Complexity of the Role Assignment Problem

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Automata, Languages and Programming (ICALP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2719))

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Abstract

A graph G is R-role assignable if there is a locally surjective homomorphism from G to R, i.e. a vertex mapping r : V G → V R, such that the neighborhood relation is preserved: r(N G (u)) = N R(r(u)). Kristiansen and Telle conjectured that the decision problem whether such a mapping exists is an NP-complete problem for any connected graph R on at least three vertices. In this paper we prove this conjecture, i.e. we give a complete complexity classification of the role assignment problem for connected graphs. We show further corollaries for disconnected graphs and related problems.

This author was partially supported by research grant GAUK 158/99.

This author was partially supported by NWO grant R 61-507 and by Czech research grant GAČR 201/99/0242 during his stay at DIMATIA center in Prague.

Supported by the Ministry of Education of the Czech Republic as project LN00A056.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Physics, DIMATIA and Institute for Theoretical Computer Science (ITI), Charles University, Malostranské nám. 2/25, 118 00, Prague, Czech Republic

    Jiří Fiala

  2. Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Daniël Paulusma

Authors
  1. Jiří Fiala
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  2. Daniël Paulusma
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA, 30332-0205, USA

    Jan Karel Lenstra

  3. Department of Information Technology, Uppsala University, P.O. Box 337, 75105, Uppsala, Sweden

    Joachim Parrow

  4. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Gerhard J. Woeginger

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© 2003 Springer-Verlag Berlin Heidelberg

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Fiala, J., Paulusma, D. (2003). The Computational Complexity of the Role Assignment Problem. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_64

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  • DOI: https://doi.org/10.1007/3-540-45061-0_64

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40493-4

  • Online ISBN: 978-3-540-45061-0

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