Elsevier

Theoretical Computer Science

Volume 522, 20 February 2014, Pages 85-94
Theoretical Computer Science

Matching and Weighted P2-Packing: Algorithms and Kernels

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Abstract

Parameterized algorithms and kernelization algorithms are presented for the weighted P2-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 P2-packings in bipartite graphs; (2) an effective graph bi-partitioning algorithm; and (3) a polynomial-time algorithm for a constrained weighted P2-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(k2) is presented, where k is the given parameter of the problem.

Keywords

Parameterized algorithm
Kernelization
Weighted P2-Packing
Matching

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A preliminary version of this work was reported in the Proceedings of the 17th Annual International Computing and Combinatorics Conference, Lecture Notes in Computer Science, vol. 6842, 2011, pp. 343–353. This work is supported by the National Natural Science Foundation of China under Grants 61232001, 61103033, 61173051, 71221061.