Improved Deterministic Algorithms for Weighted Matching and Packing Problems

Authors:
Qilong Feng;Yang Liu;Songjian Lu;Jianxin Wang
Affiliations:
School of Information Science and Engineering, Central South University, Changsha, P.R. China 410083;Department of Computer Science and Engineering, Texas A&M University, USA 77843-3112;Department of Computer Science and Engineering, Texas A&M University, USA 77843-3112;School of Information Science and Engineering, Central South University, Changsha, P.R. China 410083
Venue:
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Year:
2009

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Abstract

For the weighted r D-Matching problem, we present a deterministic parameterized algorithm with time complexity O *(4(r *** 1)k ), improving the previous best upper bound O *(4 rk ). In particular, the algorithm can be applied to solve the unweighted 3D-Matching problem with time O *(16 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(2r *** 1)k ), improving the previous best result O *(22rk ). The algorithm, when applied to the unweighted 3-Set Packing problem, has running time O *(32 k ), improving the previous best result O *(43.62 k ). Moreover, for the weighted r D-Matching and weighted r -Set Packing problems, we get a kernel of size O (k r ).