The location-dispatching problem: Polyhedral results and content delivery network design

Authors:
Philippe Chrétienne;Pierre Fouilhoux;Eric Gourdin;Jean-Mathieu Segura
Affiliations:
Laboratoire LIP6, Université Pierre et Marie Curie, 4 place Jussieu 75005 Paris, France;Laboratoire LIP6, Université Pierre et Marie Curie, 4 place Jussieu 75005 Paris, France;Orange Labs, France Telecom R&D, 38-40 bd du Géénéral Leclerc, 92794 Issy-les-Moulineaux Cedex 9, France;Laboratoire LIP6, Université Pierre et Marie Curie, 4 place Jussieu 75005 Paris, France and Orange Labs, France Telecom R&D, 38-40 bd du Géénéral Leclerc, 92794 Issy-les-Moulin ...
Venue:
Discrete Applied Mathematics
Year:
2014

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Abstract

Let G=(V,A) be a directed graph and F be a set of items. The Location-Dispatching Problem consists of determining subsets L"i@?F located at nodes i@?V, minimizing the sum of two costs: a piecewise linear installation cost associated with L"i and an access cost for each node of V to reach a copy of each item of F. We formulate this problem as a linear program with binary variables x and integer variables z. We propose a facial study of the associated polytope and we introduce the so-called integrity hop cost inequalities that force z to be an integer as soon as x is binary. Using this, we devise a branch-and-cut algorithm and report some experimental results. This algorithm has been used to solve Content Delivery Network instances in order to optimize a Video On Demand (VoD) system.