A branch-and-cut for the Non-Disjoint m-Ring-Star Problem. Issue 2 (7th March 2014)

• Record Type: Journal Article
• Authors: Fouilhoux, Pierre; Questel, Aurélien
• Is Part Of: RAIRO. Volume 48:Issue 2(2014)
• Page Start: 167
• Page End: 188
• Publication Date: 2014-03-07
• Subjects: Realistic SDH network, -- non-disjointm-ring-star problem, -- polyhedral approach, -- branch-and-cut algorithm; Operations research -- Periodicals; 658.4034
• DOI: 10.1051/ro/2014006
• Languages: English
• ISSNs: 0399-0559

Abstract

Abstract : 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.