On Complexity of Minimum Leaf Out-branching Problem

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dc.creatorDankelmann, Peter
dc.creatorGutin, Gregory
dc.creatorKim, Eun Jung
dc.date2008-08-07
dc.date.accessioned2026-07-07T09:55:22Z
dc.date.available2026-07-07T09:55:22Z
dc.descriptionGiven a digraph $D$, the Minimum Leaf Out-Branching problem (MinLOB) is the problem of finding in $D$ an out-branching with the minimum possible number of leaves, i.e., vertices of out-degree 0. Gutin, Razgon and Kim (2008) proved that MinLOB is polynomial time solvable for acyclic digraphs which are exactly the digraphs of directed path-width (DAG-width, directed tree-width, respectively) 0. We investigate how much one can extend this polynomiality result. We prove that already for digraphs of directed path-width (directed tree-width, DAG-width, respectively) 1, MinLOB is NP-hard. On the other hand, we show that for digraphs of restricted directed tree-width (directed path-width, DAG-width, respectively) and a fixed integer $k$, the problem of checking whether there is an out-branching with at most $k$ leaves is polynomial time solvable.
dc.identifierhttps://arxiv.org/abs/0808.0980
dc.identifierhttp://arxiv.org/abs/0808.0980
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/166604
dc.subjectData Structures and Algorithms
dc.subjectComputational Complexity
dc.titleOn Complexity of Minimum Leaf Out-branching Problem
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