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An efficient fixed-parameter algorithm for 3-hitting set. (English) Zbl 1118.68511
Summary: Given a collection \(C\) of subsets of size three of a finite set \(S\) and a positive integer \(k\), the 3-Hitting Set problem is to determine a subset \(S^{\prime} \subseteq S\) with \(|S^{\prime}| \leqslant k\), so that \(S^{\prime}\) contains at least one element from each subset in \(C\). The problem is NP-complete, and is motivated, for example, by applications in computational biology. Improving previous work, we give an O\((2.270^{k}+n)\) time algorithm for 3-Hitting Set, which is efficient for small values of \(k\), a typical occurrence in some applications. For \(d\)-Hitting Set we present an O\((c^{k}+n)\) time algorithm with \(c=d - 1+\mathrm O(d^{ - 1})\).

MSC:
68Q25 Analysis of algorithms and problem complexity
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