Algorithm for Finding k-Vertex Out-trees and Its Application to k-Internal Out-branching Problem
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چکیده
An out-tree T is an oriented tree with only one vertex of in-degree zero. A vertex x of T is internal if its out-degree is positive. We design randomized and deterministic algorithms for deciding whether an input digraph contains a given out-tree with k vertices. The algorithms are of runtime O∗(5.704k) and O∗(5.704k(1+o(1))), respectively. We apply the deterministic algorithm to obtain a deterministic algorithm of runtime O∗(ck), where c is a constant, for deciding whether an input digraph contains a spanning out-tree with at least k internal vertices. This answers in affirmative a question of Gutin, Razgon and Kim (Proc. AAIM’08).
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تاریخ انتشار 2009