Parameterized algorithms for weighted matching and packing problems

Authors:
Jianxin Wang;Yunlong Liu
Affiliations:
School of Information Science and Engineering, Central South University, Changsha 410083, PR China;School of Information Science and Engineering, Central South University, Changsha 410083, PR China
Venue:
Discrete Optimization
Year:
2008

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Abstract

The weighted m-d matching and m-set packing problems (m=3) are usually solved through approximation algorithms. In this paper, we define the parameterized versions of these problems and study their algorithms. For the weighted m-set packing problem, we develop a parameterized algorithm of running time O(12.8^m^kn^O^(^1^)), which is based on the recently improved color-coding technology and dynamic programming. By refining the techniques, we also develop a more efficient parameterized algorithm of running time O(12.8^(^m^-^1^)^kn^O^(^1^)) for the weighted m-d matching problem, which is a restricted version of the weighted m-set packing problem.