Improved deterministic algorithms for weighted matching and packing problems

  • Authors:

  • Jianer Chen;Qilong Feng;Yang Liu;Songjian Lu;Jianxin Wang

  • Affiliations:

  • School of Information Science and Engineering, Central South University, Changsha 410083, PR China and Department of Computer Science and Engineering, Texas A&M University, College Station, TX 778 ...;School of Information Science and Engineering, Central South University, Changsha 410083, PR China;Department of Computer Science, University of Texas-Pan American, Edinburg, TX 78539, USA;Department of Computer Science and Engineering, Texas A&M University, College Station, TX 77843, USA;School of Information Science and Engineering, Central South University, Changsha 410083, PR China

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2011

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Abstract

Based on the method of (n,k)-universal sets, we present a deterministic parameterized algorithm for the weighted rd-matching problem with time complexity O^*(4^(^r^-^1^)^k^+^o^(^k^)), improving the previous best upper bound O^*(4^r^k^+^o^(^k^)). In particular, the algorithm applied to the unweighted 3d-matching problem results in a deterministic algorithm with time O^*(16^k^+^o^(^k^)), improving the previous best result O^*(21.26^k). For the weighted r-set packing problem, we present a deterministic parameterized algorithm with time complexity O^*(2^(^2^r^-^1^)^k^+^o^(^k^)), improving the previous best result O^*(2^2^r^k^+^o^(^k^)). The algorithm, when applied to the unweighted 3-set packing problem, has running time O^*(32^k^+^o^(^k^)), improving the previous best result O^*(43.62^k^+^o^(^k^)). Moreover, for the weighted r-set packing and weighted rd-matching problems, we give a kernel of size O(k^r), which is the first kernelization algorithm for the problems on weighted versions.