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International Workshop on Approximation Algorithms for Combinatorial Optimization

International Workshop on Randomization and Approximation Techniques in Computer Science

APPROX 2005, RANDOM 2005: Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques pp 52–61Cite as

Packing Element-Disjoint Steiner Trees

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3624))

Abstract

Given an undirected graph G(V,E) with terminal set T ⊆ V the problem of packing element-disjoint Steiner trees is to find the maximum number of Steiner trees that are disjoint on the nonterminal nodes and on the edges. The problem is known to be NP-hard to approximate within a factor of Ω(logn), where n denotes |V|. We present a randomized O(logn)-approximation algorithm for this problem, thus matching the hardness lower bound. Moreover, we show a tight upper bound of O(logn) on the integrality ratio of a natural linear programming relaxation.

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Author information

Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, N2L3G1, Canada

    Joseph Cheriyan

  2. Department of Computing Science, University of Alberta, Edmonton, Alberta, T6G2E8, Canada

    Mohammad R. Salavatipour

Authors
  1. Joseph Cheriyan
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  2. Mohammad R. Salavatipour
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science, University of Illinois, 61801, Urbana, IL

    Chandra Chekuri

  2. Institute for Computer Science, University of Kiel, Olshausenstrasse 40, 24118, Kiel, Germany

    Klaus Jansen

  3. Battelle Bâtiment A, Centre Universitaire d’Informatique, Route de Drize 7, 1227, Carouge, Geneva, Switzerland

    José D. P. Rolim

  4. UC Berkeley,  

    Luca Trevisan

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© 2005 Springer-Verlag Berlin Heidelberg

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Cheriyan, J., Salavatipour, M.R. (2005). Packing Element-Disjoint Steiner Trees. In: Chekuri, C., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2005 2005. Lecture Notes in Computer Science, vol 3624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538462_5

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  • DOI: https://doi.org/10.1007/11538462_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28239-6

  • Online ISBN: 978-3-540-31874-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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