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Fixed-Parameter Approximation: Conceptual Framework and Approximability Results

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(2O((1−ε/O(1))k) p(n)) for any small ε>0.

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Author information

Correspondence to Xiuzhen Huang.

Additional information

A preliminary version of this paper was presented at the Second International Workshop on Parameterized and Exact Computation (IWPEC’06), Lecture Notes in Computer Science 4169, pp. 96–108, Zurich, Switzerland, September 13–15, 2006.

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Cai, L., Huang, X. Fixed-Parameter Approximation: Conceptual Framework and Approximability Results. Algorithmica 57, 398–412 (2010). https://doi.org/10.1007/s00453-008-9223-x

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Keywords

  • Fixed parameter computation
  • Fixed-parameter approximation
  • Fixed-parameter tractability
  • Approximation algorithm
  • Approximation scheme