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Algorithms for Finding a Maximum Non-k-linked Graph

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Algorithms – ESA 2011 (ESA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6942))

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Abstract

A graph with at least 2k vertices is said to be k-linked if for any ordered k-tuples (s 1, …, s k ) and (t 1, …, t k ) of 2k distinct vertices, there exist pairwise vertex-disjoint paths P 1, …, P k such that P i connects s i and t i for i = 1, …, k. For a given graph G, we consider the problem of finding a maximum induced subgraph of G that is not k-linked. This problem is a common generalization of computing the vertex-connectivity and testing the k-linkedness of G, and it is closely related to the concept of H-linkedness. In this paper, we give the first polynomial-time algorithm for the case of k = 2, whereas a similar problem that finds a maximum induced subgraph without 2-vertex-disjoint paths connecting fixed terminal pairs is NP-hard. For the case of general k, we give an (8k − 2)-additive approximation algorithm. We also investigate the computational complexities of the edge-disjoint case and the directed case.

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Author information

Authors and Affiliations

  1. Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Japan

    Yusuke Kobayashi

  2. School of Informatics, Kyoto University, and Preferred Infrastructure, Inc., Japan

    Yuichi Yoshida

Authors
  1. Yusuke Kobayashi
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  2. Yuichi Yoshida
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, University of Rome " La Sapienza", via Ariosto 25, 00185, Roma, Italy

    Camil Demetrescu

  2. School of Computer Science, Reykjavik University, Menntavegur 1, 101, Reykjavik, Iceland

    Magnús M. Halldórsson

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© 2011 Springer-Verlag Berlin Heidelberg

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Kobayashi, Y., Yoshida, Y. (2011). Algorithms for Finding a Maximum Non-k-linked Graph. In: Demetrescu, C., Halldórsson, M.M. (eds) Algorithms – ESA 2011. ESA 2011. Lecture Notes in Computer Science, vol 6942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23719-5_12

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  • DOI: https://doi.org/10.1007/978-3-642-23719-5_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23718-8

  • Online ISBN: 978-3-642-23719-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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