Fixed-Parameter Approximation: Conceptual Framework and Approximability Results

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 fixedparameter 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- /O(1))k) p(n)) for any small > 0.

• Type: Journal
• Year: 2010
• Where: ALGORITHMICA
• Authors: Liming Cai, Xiuzhen Huang
• Keywords: ALGORITHMICA 2010, Computations, Fixed-parameter Approximation, Fixed-parameter Computation