Polynomial time approximation schemes and parameterized complexity

  • Authors:

  • Jianer Chen;Xiuzhen Huang;Iyad A. Kanj;Ge Xia

  • Affiliations:

  • Department of Computer Science, Texas A&M University, College Station, TX 77843, USA and College of Information Science and Engineering, Central South University, Changsha 410083, PR China;Department of Computer Science, Arkansas State University, State University, AR 72467, USA;School of CTI, DePaul University, 243 S. Wabash Avenue, Chicago, IL 60604, USA;Department of Computer Science, Lafayette College, Easton, PA 18042, USA

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2007

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Abstract

In this paper, we study the relationship between the approximability and the parameterized complexity of NP optimization problems. We introduce a notion of polynomial fixed-parameter tractability and prove that, under a very general constraint, an NP optimization problem has a fully polynomial time approximation scheme if and only if the problem is polynomial fixed-parameter tractable. By enforcing a constraint of planarity on the W-hierarchy studied in parameterized complexity theory, we obtain a class of NP optimization problems, the planar W-hierarchy, and prove that all problems in this class have efficient polynomial time approximation schemes (EPTAS). The planar W-hierarchy seems to contain most of the known EPTAS problems, and is significantly different from the class introduced by Khanna and Motwani in their efforts in characterizing optimization problems with polynomial time approximation schemes.