Improved Deterministic Algorithms for Weighted Matching and Packing Problems

Qilong Feng, Yang Liu, Songjian Lu, Jianxin Wang

Abstract: For the weighted rD-Matching problem, we present a deterministic parameterized algorithm with time complexity O *(4(r − 1)k), improving the previous best upper bound O *(4rk). In particular, the algorithm can be applied to solve the unweighted 3D-Matching problem with time O *(16k), improving the previous best result O *(21.26k). 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 *(32k), improving the previous best result O *(43.62k). Moreover, for the weighted rD-Matching and weighted r-Set Packing problems, we get a kernel of size O(k r).