Fatiha Bendali

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.

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.

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.

Compatability between intervals structures and partial orderings

Compatibility between interval structures and partial orderings. If H = (X, E) is a hypergraph, n the cardinality of X, I, the ordered set { 1. . n} and < an order relation on X, we call F(X, <) the set of the one-to-one functions from X to I, which are compatible with <. If A c I, we denote by 1(A) the length of the smallest interval of I, which contains A. We first deal with the following problem: FindfEF(X, <) which minimise zmin(f)=CeeE a,* I(f(e)). The a,, eeR are positive coefficients. This problem can be understood as a scheduling problem and is checked to be NP-complete. We learn how to recognize in polynomial time those hypergraphs H =(X, E) which induce an optimal value of z min equal to CeeE a, * le 1. Next we work on a dual question which arises about interval graphs, when some partial orderings on the vertex set of these graphs intend to represent inclusion, overlapping or anteriority relations between closed intervals of the real line.Abstract Compatibility between interval structures and partial orderings. If H=(X,E) is a hypergraph, n the cardinality of X,In the ordered set {1..n} and We first deal with the following problem: Find ƒ∈F(X, which minimise zmin(ƒ)= ∑ eϵE a e ∗ɭ(ƒ(e)) . The ae, e∈R are positive coefficients. This problem can be understood as a scheduling problem and is checked to be NP-complete. We learn how to recognize in polynomial time those hypergraphs H=(X,E) which induce an optimal value of z min equal to ∑ e∈E a e ∗|e| . Next we work on a dual question which arises about interval graphs, when some partial orderings on the vertex set of these graphs intend to represent inclusion, overlapping or anteriority relations between closed intervals of the real line.