Fixed-parameter approximation: conceptual framework and approximability results

  • Authors:

  • Liming Cai;Xiuzhen Huang

  • Affiliations:

  • Department of Computer Science, The University of Georgia, Athens, Georgia;Department of Computer Science, Arkansas State University, Arkansas

  • Venue:
  • IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
  • Year:
  • 2006

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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.