Deterministic Parameterized Algorithms for Matching and Packing Problems
Abstract
We present three deterministic parameterized algorithms for well-studied packing and matching problems, namely, Weighted q-Dimensional p-Matching ((q,p)-WDM) and Weighted q-Set p-Packing ((q,p)-WSP). More specifically, we present an O*(2.85043^{(q-1)p}) time deterministic algorithm for (q,p)-WDM, an O*(8.04143^p) time deterministic algorithm for the unweighted version of (3,p)-WDM, and an O*((0.56201\cdot 2.85043^q)^p) 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(e^qq(p-1)^q) for (q,p)-WDM and (q,p)-WSP, improving the previously best known kernels of size O(q!q(p-1)^q) for these problems.
Keywords
Cite
@article{arxiv.1311.0484,
title = {Deterministic Parameterized Algorithms for Matching and Packing Problems},
author = {Meirav Zehavi},
journal= {arXiv preprint arXiv:1311.0484},
year = {2013}
}
Comments
Consideration for replacement: A better bound on the running time of WSP-Alg (see Section 5)