Deterministic Parameterized Algorithms for Matching and Packing Problems

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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*(8.04143p) time deterministic algorithm for the unweighted version of (3,p)-WDM, and an O*((0.56201. 2.85043(q-1)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(eqq(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.
Original languageEnglish
JournalArxiv preprint
Issue number1311.0484 [cs.DS]
StatePublished - 2013

Keywords

  • cs.DS

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