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In this article we study the realistic network topology of Synchronous Digital Hierarchy (SDH) networks. We describe how providers fulfill customer connectivity requirements. We show that SDH Network design reduces to the Non-Disjoint m-Ring-Star Problem (NDRSP). We first show that there is no two-index integer formulation for this problem. We then present a natural 3-index formulation for the NDRSP together with some classes of valid inequalities that are used as cutting planes in a Branch-and-Cut approach. We propose a polyhedral study of a polytope associated with this formulation. Finally, we present our Branch-and-Cut algorithm and give some experimental results on both random and real instances.
Keywords: realistic SDH network, non-disjointm-ring-star problem, polyhedral approach, branch-and-cut algorithm
@article{RO_2014__48_2_167_0,
author = {Fouilhoux, Pierre and Questel, Aur\'elien},
title = {A branch-and-cut for the {Non-Disjoint} $m${-Ring-Star} {Problem}},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {167--188},
publisher = {EDP-Sciences},
volume = {48},
number = {2},
year = {2014},
doi = {10.1051/ro/2014006},
zbl = {1292.90069},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2014006/}
}
TY - JOUR AU - Fouilhoux, Pierre AU - Questel, Aurélien TI - A branch-and-cut for the Non-Disjoint $m$-Ring-Star Problem JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2014 SP - 167 EP - 188 VL - 48 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro/2014006/ DO - 10.1051/ro/2014006 LA - en ID - RO_2014__48_2_167_0 ER -
%0 Journal Article %A Fouilhoux, Pierre %A Questel, Aurélien %T A branch-and-cut for the Non-Disjoint $m$-Ring-Star Problem %J RAIRO - Operations Research - Recherche Opérationnelle %D 2014 %P 167-188 %V 48 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro/2014006/ %R 10.1051/ro/2014006 %G en %F RO_2014__48_2_167_0
Fouilhoux, Pierre; Questel, Aurélien. A branch-and-cut for the Non-Disjoint $m$-Ring-Star Problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 2, pp. 167-188. doi: 10.1051/ro/2014006
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