Matching and P_2-Packing: Weighted Versions

摘要

Parameterized algorithms are presented for the weighted P2-Packing problem, which is a generalization of the famous Graph Matching problem. The 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 P2-Packing problem in bipartite graphs. 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.