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International Colloquium on Automata, Languages, and Programming

ICALP 2001: Automata, Languages and Programming pp 273–284Cite as

Subexponential Parameterized Algorithms Collapse the W-Hierarchy

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2076))

Abstract

It is shown that for essentially all MAX SNP-hard optimization problems finding exact solutions in subexponential time is not possible unless W[1] = FPT. In particular, we show that O(2°(k) p(n)) parameterized algorithms do not exist for VERTEX COVER, MAX CUT, MAX C-SAT, and a number of problems on bounded degree graphs such as DOMINATING SET and INDEPENDENT SET, unless W[1] = FPT. Our results are derived via an approach that uses an extended parameterization of optimization problems and associated techniques to relate the parameterized complexity of problems in FPT to the parameterized complexity of extended versions that are W[1]-hard.

This work was supported in part by the National Science Foundation research grant CCR-000248.

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Author information

Authors and Affiliations

  1. School of Electrical Engineering and Computer Science, Ohio University, Athens, OH, 45701

    Liming Cai

  2. School of Electrical Engineering and Computer Science, Ohio University, Athens, OH, 45701

    David Juedes

Authors
  1. Liming Cai
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  2. David Juedes
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Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informátics, Univ. Politècnica de Catalunya, C/Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Fernando Orejas

  2. Computer Technology Institute (CTI), University of Patras, 61 Riga Feraiou street, 26221, Patras, Greece

    Paul G. Spirakis

  3. Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584, CH, Utrecht, The Netherlands

    Jan van Leeuwen

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© 2001 Springer-Verlag Berlin Heidelberg

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Cai, L., Juedes, D. (2001). Subexponential Parameterized Algorithms Collapse the W-Hierarchy. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_23

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  • DOI: https://doi.org/10.1007/3-540-48224-5_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42287-7

  • Online ISBN: 978-3-540-48224-6

  • eBook Packages: Springer Book Archive

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