A randomized approximation algorithm for parameterized 3-D matching counting problem

  • Authors:

  • Yunlong Liu;Jianer Chen;Jianxin Wang

  • Affiliations:

  • College of Information Science and Engineering, Central South University, Changsha, P.R. China and School of Further Education, Hunan Normal University, Changsha, P.R. China;College of Information Science and Engineering, Central South University, Changsha, P.R. China and Department of Computer Science Texas A&M University, TX;College of Information Science and Engineering, Central South University, Changsha, P.R. China

  • Venue:
  • COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
  • Year:
  • 2007

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Abstract

The computational complexity of counting the number of matchings of size k in a given triple set remains open, and it is conjectured that the problem is infeasible. In this paper, we present a fixed parameter tractable randomized approximation scheme (FPTRAS) for the problem. More precisely, we develop a randomized algorithm that, on given positive real numbers ε and δ, and a given set S of n triples and an integer k, produces a number h in time O(5.483kn2 ln(2/δ)/ε2) such that prob[(1 - ε)h0 ≤ h ≤ (1 + ε)h0] 1 - δ where h0 is the total number of matchings of size k in the triple set S. Our algorithm is based on the recent improved color-coding techniques and the Monte-Carlo self-adjusting coverage algorithm developed by Karp and Luby.