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International Symposium on Parameterized and Exact Computation

IPEC 2012: Parameterized and Exact Computation pp 206–217Cite as

On the Space Complexity of Parameterized Problems

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7535)

Abstract

Parameterized complexity theory measures the complexity of computational problems predominantly in terms of their parameterized time complexity. The purpose of the present paper is to demonstrate that the study of parameterized space complexity can give new insights into the complexity of well-studied parameterized problems like the feedback vertex set problem. We show that the undirected and the directed feedback vertex set problems have different parameterized space complexities, unless L = NL; which explains why the two problem variants seem to necessitate different algorithmic approaches even though their parameterized time complexity is the same. For a number of further natural parameterized problems, including the longest common subsequence problem and the acceptance problem for multi-head automata, we show that they lie in or are complete for different parameterized space classes; which explains why previous attempts at proving completeness of these problems for parameterized time classes have failed.

Keywords

  • parameterized complexity theory
  • logarithmic space
  • fixed-parameter tractable problems
  • feedback vertex set
  • reachability problems

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  • DOI: 10.1007/978-3-642-33293-7_20
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Author information

Authors and Affiliations

  1. Institute for Theoretical Computer Science, Universität zu Lübeck, D-23562, Lübeck, Germany

    Michael Elberfeld, Christoph Stockhusen & Till Tantau

Authors
  1. Michael Elberfeld
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  2. Christoph Stockhusen
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  3. Till Tantau
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Editor information

Editors and Affiliations

  1. Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, 15784, Athens, Greece

    Dimitrios M. Thilikos

  2. Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Gerhard J. Woeginger

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Elberfeld, M., Stockhusen, C., Tantau, T. (2012). On the Space Complexity of Parameterized Problems. In: Thilikos, D.M., Woeginger, G.J. (eds) Parameterized and Exact Computation. IPEC 2012. Lecture Notes in Computer Science, vol 7535. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33293-7_20

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  • DOI: https://doi.org/10.1007/978-3-642-33293-7_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33292-0

  • Online ISBN: 978-3-642-33293-7

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