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- W1863153721 abstract "Let $M = (E, {cal I})$ be a matroid, and let ${cal S}$ be a family of subsets of size $p$ of $E$. A subfamily $widehat{cal S} subseteq {cal S}$ represents ${cal S}$ if for every pair of sets $X in {cal S}$ and $Y subseteq E setminus X$ such that $X cup Y in {cal I}$, there is a set $widehat{X} in widehat{cal S}$ disjoint from $Y$ such that $widehat{X} cup Y in {cal I}$. In this paper, we present a fast computation of representative families for uniform matroids. We use our computation to develop {em deterministic} algorithms that solve {sc $k$-Partial Cover} and {sc $k$-Internal Out-Branching} in times $O^*(2.619^k)$ and $O^*(6.855^k)$, respectively. We thus significantly improve the best known {em randomized} algorithm for {sc $k$-Partial Cover} and {em deterministic} algorithm for {sc $k$-Internal Out-Branching}, that run in times $O^*(5.437^k)$ and $O^*(16^{k+o(k)})$, respectively. Finally, we improve the running times of several algorithms that rely on efficient computation of representative families." @default.
- W1863153721 created "2016-06-24" @default.
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- W1863153721 date "2014-02-14" @default.
- W1863153721 modified "2023-10-14" @default.
- W1863153721 title "Faster Computation of Representative Families for Uniform Matroids with Applications." @default.
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