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Fixed-Parameter Approximation: Conceptual Framework and Approximability Results

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Parameterized and Exact Computation (IWPEC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4169))

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Abstract

The notion of fixed-parameter approximation is introduced to investigate the approximability of optimization problems within the framework of fixed-parameter computation. This work partially aims at enhancing the world of fixed-parameter computation in parallel with the conventional theory of computation that includes both exact and approximate computations. In particular, it is proved that fixed-parameter approximability is closely related to the approximation of small-cost solutions in polynomial time. It is also demonstrated that many fixed-parameter intractable problems are not fixed-parameter approximable. On the other hand, fixed-parameter approximation appears to be a viable approach to solving some inapproximable yet important optimization problems. For instance, all problems in the class MAX SNP admit fixed-parameter approximation schemes in time O(2\(^{O((1-{\epsilon}/{\it O}(1)){\it k})}\) p(n)) for any small ε> 0.

The authors would like to thank Rod Downey and Mike Fellows regarding the definition of the fixed-parameter approximability for the problem dominating set.

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Author information

Authors and Affiliations

  1. Department of Computer Science, The University of Georgia, Athens, Georgia, 30605, USA

    Liming Cai

  2. Department of Computer Science, Arkansas State University, Arkansas, 72467, USA

    Xiuzhen Huang

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  1. Liming Cai
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  2. Xiuzhen Huang
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Editor information

Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, The Netherlands

    Hans L. Bodlaender

  2. University of Tennessee, 37996-3450, Knoxville, Tennessee, U.S.A.

    Michael A. Langston

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© 2006 Springer-Verlag Berlin Heidelberg

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Cai, L., Huang, X. (2006). Fixed-Parameter Approximation: Conceptual Framework and Approximability Results. In: Bodlaender, H.L., Langston, M.A. (eds) Parameterized and Exact Computation. IWPEC 2006. Lecture Notes in Computer Science, vol 4169. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11847250_9

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  • DOI: https://doi.org/10.1007/11847250_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-39098-5

  • Online ISBN: 978-3-540-39101-2

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