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Algorithms for k-Internal Out-Branching

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Parameterized and Exact Computation (IPEC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8246))

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Abstract

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 *(4k) 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 \(O^*(2^{(2-\frac{\Delta+1}{\Delta(\Delta-1)})k})\) time randomized algorithm for k-IOB. Both our algorithms use polynomial space.

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Author information

Authors and Affiliations

  1. Department of Computer, Science Technion - Israel Institute of Technology, Haifa, 32000, Israel

    Meirav Zehavi

Authors
  1. Meirav Zehavi
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Editor information

Editors and Affiliations

  1. Royal Holloway, University of London, Egham Hill, TW20 0EX, Egham, UK

    Gregory Gutin

  2. Institute of Information Systems, Vienna University of Technology, (184/3), Favoritenstraße 9-11, 1040, Vienna, Austria

    Stefan Szeider

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© 2013 Springer International Publishing Switzerland

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Zehavi, M. (2013). Algorithms for k-Internal Out-Branching. In: Gutin, G., Szeider, S. (eds) Parameterized and Exact Computation. IPEC 2013. Lecture Notes in Computer Science, vol 8246. Springer, Cham. https://doi.org/10.1007/978-3-319-03898-8_30

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  • DOI: https://doi.org/10.1007/978-3-319-03898-8_30

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03897-1

  • Online ISBN: 978-3-319-03898-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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