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k-Edge-Connectivity: Approximation and LP Relaxation

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Approximation and Online Algorithms (WAOA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6534))

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Abstract

In the k-edge-connected spanning subgraph problem we are given a graph (V, E) and costs for each edge, and want to find a minimum-cost F ⊂ E such that (V, F) is k-edge-connected. We show there is a constant ε> 0 so that for all k > 1, finding a (1 + ε)-approximation for k-ECSS is NP-hard, establishing a gap between the unit-cost and general-cost versions. Next, we consider the multi-subgraph cousin of k-ECSS, in which we purchase a multi-subset F of E, with unlimited parallel copies available at the same cost as the original edge. We conjecture that a (1 + Θ(1/k))-approximation algorithm exists, and we describe an approach based on graph decompositions applied to its natural linear programming (LP) relaxation. The LP is essentially equivalent to the Held-Karp LP for TSP and the undirected LP for Steiner tree. We give a family of extreme points for the LP which are more complex than those previously known.

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Author information

Authors and Affiliations

  1. École Polytechnique Fédérale de Lausanne, Switzerland

    David Pritchard

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  1. David Pritchard
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Editors and Affiliations

  1. Department of Computer Science, University of Kiel, Olshausenstrasse 40, 24118, Kiel, Germany

    Klaus Jansen

  2. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, Ontario, Canada

    Roberto Solis-Oba

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Pritchard, D. (2011). k-Edge-Connectivity: Approximation and LP Relaxation. In: Jansen, K., Solis-Oba, R. (eds) Approximation and Online Algorithms. WAOA 2010. Lecture Notes in Computer Science, vol 6534. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18318-8_20

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  • DOI: https://doi.org/10.1007/978-3-642-18318-8_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18317-1

  • Online ISBN: 978-3-642-18318-8

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