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International audience; One of the challenges of cloud computing is to assign virtual machines to physical machines optimally and efficiently. The aim of telecommunication operators is to minimize the mapping cost while respecting constraints regarding location, assignment and capacity. We formulate this problem which appears to be a quadratic constrained non-convex 0-1 program. Then, we propose to lift the problem to a higher dimensional space by classical linearization, thereby handling the problem in the framework of MIP. To improve its computational performance, we employ the Reformulation-Linearization-Technique (RLT) and add valid inequalities to strengthen the model. Some preliminary numerical experiments are conducted to show the effectiveness of these methods

International audience; The maximum cut problem is a classical combinatorial optimization problem that is known to be NP-hard in general. In the present article, we provide some new lower and upper bounds that are based on the eigenvalues of the weight matrix with modified diagonal entries. Namely, we show that some upper bounds presented here are generally better than the SDP bound introduced by Goemans and Williamson, JACM 42 (1995), 1115-1145. We also discuss the complexity of computing these bounds and provide some preliminary computational results

International audience; One popular approach to overcome the expected congestions due to the spectacular development of various multimedia applications consists in installing transparent caches at strategically chosen places inside telecommunication networks. The problem of locating caches is a difficult optimization problem, closely related to the p-median problem. In the case where the network is a tree, some cache location problems have already been investigated. In this paper, we propose to refine these models by taking into account a dynamic effect due to cache replacement policies. In our model, only the most popular contents are stored in the caches. The hierarchical effect of several successive caches is also captured by the model. A Mixed Integer Programming model and a Dynamic Programming algorithm are proposed and compared on a preliminary set of numerical experiments.