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The Complexity of Three-Element Min-Sol and Conservative Min-Cost-Hom

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Automata, Languages, and Programming (ICALP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7965))

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Abstract

Thapper and Živný [STOC’13] recently classified the complexity of VCSP for all finite-valued constraint languages. However, the complexity of VCSPs for constraint languages that are not finite-valued remains poorly understood. In this paper we study the complexity of two such VCSPs, namely Min-Cost-Hom and Min-Sol. We obtain a full classification for the complexity of Min-Sol on domains that contain at most three elements and for the complexity of conservative Min-Cost-Hom on arbitrary finite domains. Our results answer a question raised by Takhanov [STACS’10, COCOON’10].

A longer version of this paper is available at http://arxiv.org/abs/1301.0027

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Authors and Affiliations

  1. Department of Computer and Information Science, Linköping University, SE-581 83, Linköping, Sweden

    Hannes Uppman

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  1. Hannes Uppman
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Postboks 7803, 5020, Bergen, Norway

    Fedor V. Fomin

  2. Faculty of Computing, University of Latvia, Raina bulv. 19, 1586, Riga, Latvia

    Rūsiņš Freivalds

  3. Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Marta Kwiatkowska

  4. Faculty of Mathematics and Computer Science, Weizmann Institute of Science, POB 26, 76100, Rehovot, Israel

    David Peleg

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Uppman, H. (2013). The Complexity of Three-Element Min-Sol and Conservative Min-Cost-Hom. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39206-1_68

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  • DOI: https://doi.org/10.1007/978-3-642-39206-1_68

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39205-4

  • Online ISBN: 978-3-642-39206-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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