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Primal-Dual Approximation Algorithms for Node-Weighted Network Design in Planar Graphs

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2012, RANDOM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7408))

Abstract

We present primal-dual algorithms which give a 2.4 approximation for a class of node-weighted network design problems in planar graphs, introduced by Demaine, Hajiaghayi and Klein (ICALP’09). This class includes Node-Weighted Steiner Forest problem studied recently by Moldenhauer (ICALP’11) and other node-weighted problems in planar graphs that can be expressed using (0,1)-proper functions introduced by Goemans and Williamson. We show that these problems can be equivalently formulated as feedback vertex set problems and analyze approximation factors guaranteed by different violation oracles within the primal-dual framework developed by Goemans and Williamson.

G.Y. is supported by NSF / CCF CAREER award 0845701 and by College of Engineering Fellowship.

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Authors and Affiliations

  1. Pennsylvania State University, USA

    Piotr Berman & Grigory Yaroslavtsev

Authors
  1. Piotr Berman
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  2. Grigory Yaroslavtsev
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Carnegie Mellon University, Gates Building 7203, 15213, Pittsburgh, PA, USA

    Anupam Gupta

  2. Department of Computer Science, University Kiel, OlshausenstraĂźe 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Centre Universitaire d’Informatique, University of Geneva, Battelle A, 7 route de Drize, 1227, Carouge, Switzerland

    José Rolim

  4. Department of Computer Science, Foundation School of Engineering and Applied Science, Columbia University, Amsterdam Avenue 1214, 10027-7003, New York, NY, USA

    Rocco Servedio

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© 2012 Springer-Verlag Berlin Heidelberg

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Berman, P., Yaroslavtsev, G. (2012). Primal-Dual Approximation Algorithms for Node-Weighted Network Design in Planar Graphs. In: Gupta, A., Jansen, K., Rolim, J., Servedio, R. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2012 2012. Lecture Notes in Computer Science, vol 7408. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32512-0_5

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  • DOI: https://doi.org/10.1007/978-3-642-32512-0_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32511-3

  • Online ISBN: 978-3-642-32512-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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