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Steiner k-Edge Connected Subgraph Polyhedra

Author

Listed:
  • M. Didi Biha

    (École Polytechnique)

  • A.R. Mahjoub

    (Université de Clermont II, Complexe Scientifique des Cézeaux)

Abstract

In this paper we consider the Steiner k-edge survivable network problem. We discuss the polytope associated with the solutions to that problem. We show that when the graph is series-parallel and k is even, the polytope is completely described by the trivial constraints and the so called Steiner-cut constraints. This generalizes recent work of Baïou and Mahjoub, SIAM J. Discrete Mathematics, vol. 10, pp. 505–514, 1997 for the case k = 2. As a consequence, we obtain in this case a linear description of the polyhedron associated with the problem when multiple copies of an edge are allowed.

Suggested Citation

  • M. Didi Biha & A.R. Mahjoub, 2000. "Steiner k-Edge Connected Subgraph Polyhedra," Journal of Combinatorial Optimization, Springer, vol. 4(1), pages 131-144, March.
    • Handle: RePEc:spr:jcomop:v:4:y:2000:i:1:d:10.1023_a:1009893108387
    DOI: 10.1023/A:1009893108387
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    References listed on IDEAS

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    1. Ranel E. Erickson & Clyde L. Monma & Arthur F. Veinott, 1987. "Send-and-Split Method for Minimum-Concave-Cost Network Flows," Mathematics of Operations Research, INFORMS, vol. 12(4), pages 634-664, November.
    2. Martin Grötschel & Clyde L. Monma & Mechthild Stoer, 1992. "Computational Results with a Cutting Plane Algorithm for Designing Communication Networks with Low-Connectivity Constraints," Operations Research, INFORMS, vol. 40(2), pages 309-330, April.
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