Algorithms for k-internal out-branching

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14 Scopus citations


The k-Internal Out-Branching (k-IOB) problem asks if a given directed graph has an out-branching (i.e., a spanning tree with exactly one node of in-degree 0) with at least k internal nodes. The k-Internal Spanning Tree (k-IST) problem is a special case of k-IOB, which asks if a given undirected graph has a spanning tree with at least k internal nodes. We present an O*(4 k) time randomized algorithm for k-IOB, which improves the O* running times of the best known algorithms for both k-IOB and k-IST. Moreover, for graphs of bounded degree Δ, we present an O*(2 (2-Δ+1/Δ(Δ-1))k) time randomized algorithm for k-IOB. Both our algorithms use polynomial space.

Original languageEnglish
Title of host publicationParameterized and Exact Computation - 8th International Symposium, IPEC 2013, Revised Selected Papers
Number of pages13
StatePublished - 1 Dec 2013
Externally publishedYes
Event8th International Symposium on Parameterized and Exact Computation, IPEC 2013 - Sophia Antipolis, France
Duration: 4 Sep 20136 Sep 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8246 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference8th International Symposium on Parameterized and Exact Computation, IPEC 2013
CitySophia Antipolis


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