Jean Mailfert

Heuristics for Designing Energy-efficient Wireless Sensor Network Topologies

Wireless Sensor Networks (WSN) have been studied in several contexts. There are many challenges involving WSN design such as the energy resources optimization, the robustness and the network coverage. We address here the problem of energy-efficient topology design. A welldesigned dynamic topology and efficient routing algorithms may allow a large reduction on the energy consumption, which is one of the main concerns of WSN nodes. In this work, we propose to model the problem of clustering a WSN topology as a variation of the independent dominating set optimization problem. Then, we describe two heuristics to generate a WSN topology and two ways to evaluate the energy consumption. Computational results are presented for instances with up to 500 nodes.

An Optimization Approach for Designing Wireless Sensor Networks

Wireless sensor networks have been studied in several contexts because of their large number of applications. There are many challenges involving such networks as the energy resources optimization, the robustness and the network coverage. We address here the problem of energy efficient topology design. A well-designed dynamic topology and an efficient routing algorithm allow to reduce energy consumption, which is the main constraint of wireless sensor node. In this work, we propose to model the problem as a variation of the independent set optimization problem, for the clustering the wireless sensor nodes. We also propose a local search procedure to improve the whole network topology and a specific evaluation procedure.

Composition of graphs and the Hop-constrained Path Problem

Given a graph G = (V,E) and a non negative cost function on edges, the Hop-constrained Path Problem (HPP) consists of finding between two distinguished vertices s and t of V a minimum cost path with no more than L edges where L is a fixed integer. Dahl characterised the dominant of the convex hull of the incidence vectors of st-paths of length bounded by L, denoted by DL(G), for any graph G when L ≤ 3, using trivial, st-cut, and L-path-cut inequalities. A graph G is said L-h-simple if the set of Dahls inequalities is sufficient to define DL(G). In this paper, we study the L-h-simple property when L ≥ 4. We present some results on the facial structure of the dominant DL(G). We also examine some basic operations on graphs which preserve the L-h-simple property.

Tarification par des jeux coopératifs avec demandes élastiques

We propose here a pricing Model which is an extension of the Cooperative Game concept and which includes a notion of Elastic Demand. We present some existence results as well as some algorithms. We conclude by discussing this model in the context of some Production and Transportation problems.

Coeur et nucléolus des jeux de recouvrement

A cooperative game is defined as a set of players and a cost function. The distribution of the whole cost between the players can be done using the core concept, that is the set of all undominated cost allocations which prevent players from grouping. In this paper we study a game whose cost function comes from the optimal solution of a linear integer covering problem. We give necessary and sufficient conditions for the core to be nonempty and characterize its allocations using linear programming duality. We also discuss a special allocation, called the nucleolus. We characterize that allocation and show that it can be computed in polynomial time using a column generation method.

Half integer extreme points in the linear relaxation of the 2-edge-connected subgraph polyhedron

Abstract This paper studies the graphs for which the linear relaxation of the 2-connected spanning subgraph polyhedron has integer or half-integer extreme points. These graphs are called quasi-integer. For these graphs, the linear relaxation of the k-edge connected spanning subgraph polyhedron is integer for all k=4r, r≥1. The class of quasi-integer graphs is closed under minors and contains for instance the class of series-parallel graphs. We discuss some structural properties of graphs which are minimally non quasi-integer graphs, then we examine some basic operations which preserve the quasi-integer property. Using this, we show that the subdivisions of wheels are quasi-integer.

Extended cooperative networks games

We present here a pricing model which is an extension of the Cooperative Game concept and which includes a notion of Price-Dependent Demand. We present some existence results as well as some algorithms, and conclude by discussing a specific problem related to Network Pricing.

Cooperative networks games with elastic demands

We present here a pricing model which is an extension of the cooperative game concept and which includes a notion of elastic demand. We present some existence results as well as an algorithm, and we conclude by discussing a specific problem related to network pricing.

Composition of Graphs and the Triangle-Free Subgraph Polytope

In this paper, we study a composition (decomposition) technique for the triangle-free subgraph polytope in graphs which are decomposable by means of 3-sums satisfying some property. If a graph G decomposes into two graphs G1 and G2, we show that the triangle-free subgraph polytope of G can be described from two linear systems related to G1 and G2. This gives a way to characterize this polytope on graphs that can be recursively decomposed. This also gives a procedure to derive new facets for this polytope. We also show that, if the systems associated with G1 and G2 are TDI, then the system characterizing the polytope for G is TDI. This generalizes previous results in R. Euler and A.R. Mahjoub (Journal of Comb. Theory series B, vol. 53, no. 2, pp. 235–259, 1991) and A.R. Mahjoub (Discrete Applied Math., vol. 62, pp. 209–219, 1995).