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A branch-and-cut for the Non-Disjoint m-Ring-StarProblem

Published online by Cambridge University Press:  07 March 2014

Pierre Fouilhoux  and
Aurélien Questel
Pierre Fouilhoux
Affiliation:
Laboratoire LIP6, Université Pierre et Marie Curie, 4 place Jussieu 75005 Paris, France.. pierre.fouilhoux@lip6.fr; aurelien.questel@lip6.fr
Aurélien Questel
Affiliation:
Laboratoire LIP6, Université Pierre et Marie Curie, 4 place Jussieu 75005 Paris, France.. pierre.fouilhoux@lip6.fr; aurelien.questel@lip6.fr
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Abstract

In this article we study the realistic network topology of Synchronous Digital Hierarchy(SDH) networks. We describe how providers fulfill customer connectivity requirements. Weshow that SDH Network design reduces to the Non-Disjoint m-Ring-Star Problem (NDRSP). Wefirst show that there is no two-index integer formulation for this problem. We thenpresent a natural 3-index formulation for the NDRSP together with some classes of validinequalities that are used as cutting planes in a Branch-and-Cut approach. We propose apolyhedral study of a polytope associated with this formulation. Finally, we present ourBranch-and-Cut algorithm and give some experimental results on both random and realinstances.

Keywords

Realistic SDH networknon-disjointm-ring-star problempolyhedral approachbranch-and-cut algorithm
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 2: Isco 2012, guest editors Nelson Maculan, A. Ridha Mahjoub, Eduardo Uchoa , April 2014 , pp. 167 - 188
Copyright
© EDP Sciences, ROADEF, SMAI, 2014

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