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Annual Symposium on Theoretical Aspects of Computer Science

STACS 2001: STACS 2001 pp 431–442Cite as

Approximation Algorithms for Minimum Size 2-Connectivity Problems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2010))

Abstract

We study some versions of the problem of finding the minimum size 2-connected subgraph. This problem is NP-hard (even on cubic planar graphs) and MAX SNP-hard. We show that the minimum 2-edge connected subgraph problem can be approximated to within 4/3 -ε for general graphs, improving upon the recent result of Vempala and Vetta [14]. Better approximations are obtained for planar graphs and for cubic graphs.We also consider the generalization, where requirements of 1 or 2 edge or vertex disjoint paths are specified between every pair of vertices, and the aim is to find a minimum subgraph satisfying these re- quirements. We show that this problem can be approximated within 3/2, general- izing earlier results for 2-connectivity. We also analyze the classical local opti- mization heuristics. For cubic graphs, our results imply a new upper bound on the integrality gap of the linear programming formulation for the 2-edge connectivity problem.

Partially supported by the IST Program of the EU under contract number IST-1999-14186 (ALCOM-FT). The author was supported by Deutsche Forschungsgemeinschaft (DFG) Graduate Scholarship. Part of the work by this author was done while he was visiting the Combinatorics & Optimization Dept., University of Waterloo, Ontario, Canada, during January-March, 2000, and was partially supported by NSERC grant no. OGP0138432 of Joseph Cheriyan.

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, D-66123, Saarbrücken, Germany

    Piotr Krysta & V. S. Anil Kumar

Authors
  1. Piotr Krysta
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  2. V. S. Anil Kumar
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Editor information

Editors and Affiliations

  1. I3S & INRIA Sophia Antipolis INRIA, CNRS, 2004 Route des Lucioles, 06902, Sophia-Antipolis, France

    Afonso Ferreira

  2. Institut für Theoretische Informatik, Fakultät Informatik, TU Dresden, 01062, Dresden, Germany

    Horst Reichel

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© 2001 Springer-Verlag Berlin Heidelberg

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Krysta, P., Kumar, V.S.A. (2001). Approximation Algorithms for Minimum Size 2-Connectivity Problems. In: Ferreira, A., Reichel, H. (eds) STACS 2001. STACS 2001. Lecture Notes in Computer Science, vol 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44693-1_38

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  • DOI: https://doi.org/10.1007/3-540-44693-1_38

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41695-1

  • Online ISBN: 978-3-540-44693-4

  • eBook Packages: Springer Book Archive

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