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Finding optimum k-vertex connected spanning subgraphs: Improved approximation algorithms for k=3, 4, 5

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Algorithms and Complexity (CIAC 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1203))

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Abstract

The problem of finding a minimum weight k-vertex connected spanning subgraph is considered. For k>1, this problem is known to be NP-hard. Combining properties of inclusion-minimal k-vertex connected graphs and of k-out-connected graphs (i.e., graphs which contain a vertex from which there are k internally vertex-disjoint paths to every other vertex), we derive polynomial time approximation algorithms for several values of k.

  1. (i)

    For k=3, we give an algorithm with approximation factor 2. This improves the best previously known factor 3.

  2. (ii)

    For k=4 and k=5, we give an algorithm with approximation factor 3. This improves the best previously known factors 4 1/6 and 4 17/30, respectively.

Up to 1990, E. A. Dinic, Moscow.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, Technion, 32000, Haifa, Israel

    Yefim Dinitz

  2. Dept. of Mathematics, Technion, 32000, Haifa, Israel

    Zeev Nutov

Authors
  1. Yefim Dinitz
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  2. Zeev Nutov
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Giancarlo Bongiovanni Daniel Pierre Bovet Giuseppe Di Battista

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© 1997 Springer-Verlag Berlin Heidelberg

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Dinitz, Y., Nutov, Z. (1997). Finding optimum k-vertex connected spanning subgraphs: Improved approximation algorithms for k=3, 4, 5. In: Bongiovanni, G., Bovet, D.P., Di Battista, G. (eds) Algorithms and Complexity. CIAC 1997. Lecture Notes in Computer Science, vol 1203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62592-5_57

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  • DOI: https://doi.org/10.1007/3-540-62592-5_57

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62592-6

  • Online ISBN: 978-3-540-68323-0

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