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New Results on the Complexity of the Max- and Min-Rep Problems

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SOFSEM 2011: Theory and Practice of Computer Science (SOFSEM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6543))

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Abstract

This paper deals with the Max-Rep and Min-Rep problems, both of which are related to the famous Label Cover problem. These are of notable theoretical interest, since they are often used to prove hardness results for other problems. In many cases new complexity results for these problems may be preserved by the reductions, and so new results for Max-Rep and Min-Rep could be applicable to a wide range of other problems as well.

Both Max- and Min-Rep are strongly inapproximable, and the best approximation algorithms have a ratio of O(n 1/3) and O(n 1/3log2/3 n) respectively. Thus, other approaches are desperately needed to tackle these hard problems. In our paper we use the very successful parameterized complexity paradigm and obtain new complexity results for various parameterizations of the problems.

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Author information

Authors and Affiliations

  1. Faculty of Informatics, Masaryk University, Botanická 68a, Brno, Czech Republic

    Robert Ganian

Authors
  1. Robert Ganian
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Editor information

Editors and Affiliations

  1. Ivana Černá, Department of Computer Science, Faculty of Informatics, Faculty of Informatics, Masaryk University, Botanicka 68 a, 602 00, Brno, Czech Republic

    Ivana Černá

  2. Department of Software Engineering, University of Szeged, Árpád tér 2., 6720, Szeged, Hungary

    Tibor Gyimóthy

  3. Informationstechnologie und Ausbildung, CAB F 16, F 13.1, Universitätstraße 6, ETH Zürich, 8092, Zürich, Switzerland

    Juraj Hromkovič

  4. School of History and Anthropology, Queen’s University, 15 University Square, BT7 1NN, Belfast, UK

    Keith Jefferey

  5. Department of Computer Science, Comenius University, 84248, Bratislava, Slovakia

    Rastislav Králović

  6. EURECOM, 2229 2229 Route des Crêtes, BP 193, 06904, Sophia Antipolis cedex, France

    Marko Vukolić

  7. Institute of Theoretical Computer Science, ETH Zürich, IFW E49.1, Haldeneggsteig 4, 8092, Zürich, Switzerland

    Stefan Wolf

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Ganian, R. (2011). New Results on the Complexity of the Max- and Min-Rep Problems. In: Černá, I., et al. SOFSEM 2011: Theory and Practice of Computer Science. SOFSEM 2011. Lecture Notes in Computer Science, vol 6543. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18381-2_20

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  • DOI: https://doi.org/10.1007/978-3-642-18381-2_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18380-5

  • Online ISBN: 978-3-642-18381-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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