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Polynomial Time Approximation Schemes and Parameterized Complexity

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Mathematical Foundations of Computer Science 2004 (MFCS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3153))

Abstract

In this paper, we study the relationship between the approximability and the parameterized complexity of NP optimization problems. We introduce the notion of efficient fixed-parameter tractability and prove that, under a very general constraint, an NP optimization problem has a fully polynomial time approximation scheme if and only if the problem is efficiently fixed-parameter tractable. By enforcing a constraint of planarity on the W-hierarchy studied in parameterized complexity theory, we obtain a class of NP optimization problems, the planar W -hierarchy, and prove that all problems in this class have efficient polynomial time approximation schemes (EPTAS).

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Author information

Authors and Affiliations

  1. Department of Computer Science, Texas A&M University, College Station, TX, 77843-3112, USA

    Jianer Chen, Xiuzhen Huang & Ge Xia

  2. School of Computer Science, Telecommunications and Information Systems, DePaul University, 243 S. Wabash Avenue, Chicago, IL, 60604-2301, USA

    Iyad A. Kanj

Authors
  1. Jianer Chen
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  2. Xiuzhen Huang
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  3. Iyad A. Kanj
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  4. Ge Xia
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Editor information

Editors and Affiliations

  1. Institute for Theoretical Computer Science and Department of Applied Mathematics, Charles University, Prague, Czech Republic

    Jiří Fiala  & Jan Kratochvíl  & 

  2. Department of Theoretical Computer Science and Mathematical Logic, Faculty of Mathematics and Physics, Charles University, Malostranske nam. 25, 118 00, Praha1, Czech Republic

    Václav Koubek

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© 2004 Springer-Verlag Berlin Heidelberg

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Chen, J., Huang, X., Kanj, I.A., Xia, G. (2004). Polynomial Time Approximation Schemes and Parameterized Complexity. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds) Mathematical Foundations of Computer Science 2004. MFCS 2004. Lecture Notes in Computer Science, vol 3153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28629-5_38

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  • DOI: https://doi.org/10.1007/978-3-540-28629-5_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22823-3

  • Online ISBN: 978-3-540-28629-5

  • eBook Packages: Springer Book Archive

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