Fixed-Parameter Approximation: Conceptual Framework and Approximability Results

  • Liming Cai
  • Xiuzhen Huang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4169)


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.


Polynomial Time Minimization Problem Approximation Scheme Maximization Problem Vertex Cover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Liming Cai
    • 1
  • Xiuzhen Huang
    • 2
  1. 1.Department of Computer ScienceThe University of GeorgiaAthensUSA
  2. 2.Department of Computer ScienceArkansas State UniversityUSA

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