Matching and Weighted P2-Packing: Algorithms and Kernels

Authors:
Qilong Feng;Jianxin Wang;Jianer Chen
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;School of Information Science and Engineering, Central South University, Changsha 410083, PR China and Department of Computer Science, Texas A&M University, College Station, TX 77843-3112, USA
Venue:
Theoretical Computer Science
Year:
2014

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Abstract

Parameterized algorithms and kernelization algorithms are presented for the weighted P"2-Packing problem, which is a generalization of the famous Graph Matching problem. The parameterized algorithms are based on the following new techniques and observations: (1) new study on structure relationship between graph matchings in general graphs and P"2-packings in bipartite graphs; (2) an effective graph bi-partitioning algorithm; and (3) a polynomial-time algorithm for a constrained weighted P"2-Packing problem in bipartite graphs. The kernelization algorithms are based on the following new techniques: (1) the application of graph matching in kernelization; (2) a crown reduction structure for weighted problems. These techniques lead to randomized and deterministic parameterized algorithms that significantly improve the previous best upper bounds for the problem for both weighted and unweighted versions. For the kernelization algorithm, by using a weighted version of crown reduction, a kernel of size O(k^2) is presented, where k is the given parameter of the problem.