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dc.contributor.authorBonsma, Paul
dc.contributor.authorDorn, Frederic
dc.description.abstractAn out-branching of a directed graph is a rooted spanning tree with all arcs directed outwards from the root. We consider the problem of deciding whether a given digraph D has an out-branching with at least k leaves (Directed Spanning k-Leaf). We prove that this problem is fixed parameter tractable, when k is chosen as the parameter. Previously this was only known for restricted classes of directed graphs. The main new ingredient in our approach is a lemma that shows that given a locally optimal out-branching of a directed graph in which every arc is part of at least one out-branching, either an out-branching with at least k leaves exists, or a path decomposition with width O(k3) can be found. This enables a dynamic programming based algorithm of running time 2O(k3logk)·nO(1), where n=|V(D)|en
dc.subject.ddc510 Mathematiken
dc.subject.otherFPT algorithmen
dc.subject.othermaximum leafen
dc.subject.otherdirected graphen
dc.subject.otherspanning treeen
dc.titleAn FPT Algorithm for Directed Spanning k-Leafen
dc.typeResearch Paperen
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2007, 46en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften » Inst. Mathematikde
Appears in Collections:Technische Universität Berlin » Publications

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