Algorithm for Finding $k$-Vertex Out-trees and its Application to $k$-Internal Out-branching Problem

dc.creatorCohen, Nathann
dc.creatorFomin, Fedor V.
dc.creatorGutin, Gregory
dc.creatorKim, Eun Jung
dc.creatorSaurabh, Saket
dc.creatorYeo, Anders
dc.date2009-03-05
dc.date.accessioned2026-07-07T12:49:17Z
dc.date.available2026-07-07T12:49:17Z
dc.descriptionAn 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 $O^*(5.704^k)$ and $O^*(5.704^{k(1+o(1))})$, respectively. We apply the deterministic algorithm to obtain a deterministic algorithm of runtime $O^*(c^k)$, 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).
dc.identifierhttps://arxiv.org/abs/0903.0938
dc.identifierhttp://arxiv.org/abs/0903.0938
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222350
dc.subjectData Structures and Algorithms
dc.titleAlgorithm for Finding $k$-Vertex Out-trees and its Application to $k$-Internal Out-branching Problem
dc.typetext

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