Deterministic Parameterized Algorithms for Matching and Packing Problems

We present three deterministic parameterized algorithms for well-studied packing and matching problems, namely, Weighted q-Dimensional p-Matching ((q, p)-WDM) and Weighted qSet p-Packing ((q, p)-WSP). More specifically, we present an O(2.85043) time deterministic algorithm for (q, p)-WDM, an O(8.04143) time deterministic algorithm for the unweighted version of (3, p)-WDM, and an O((0.56201 · 2.85043)) time deterministic algorithm for (q, p)-WSP. Our algorithms significantly improve the previously best known O running times in solving (q, p)WDM and (q, p)-WSP, and the previously best known deterministic O running times in solving the unweighted versions of these problems. Moreover, we present kernels of size O(eq(p− 1)) for (q, p)-WDM and (q, p)-WSP, improving the previously best known kernels of size O(q!q(p − 1)) for these problems.