Walid Ben-Ameur

Internet Routing and Related Topology Issues

In most domains of the Internet network, the traffic demands are routed on a single-path defined as the shortest one according to a set of administrative weights. Most of the time, the values set by the administrator (or the default ones) are such that there are many paths of the same length between the extremities of some demands. However, if the shortest paths are not unique, it might become difficult for an Internet domain administrator to predict and control the traffic flows in the network. Moreover, the sequence order of packets can be changed when many paths are used leading to some end-to-end delays. It is hence an important issue to ensure that each shortest path is unique according to a given set of administrative weights. We show that it is possible to determine a set of small integer weights (smaller than 6 times the radius of the network) such that all links are used and every demand is routed on a unique shortest path. Above and beyond this uniqueness requirement, network administrators wishing to exploit the available resources would like to control the whole routing pattern. The problem they face consists of determining a set of weights enforcing a given routing policy. We formulate this problem using linear programs, and we show how integer weights can be computed by heuristics with guaranteed worst-case performances. Some conditions on the given routing, necessary for the existence of a solution, are derived. Both necessary and sufficient conditions are also provided, together with some other useful properties, in the case of particular graphs such as cycles and cacti.

Computing the Initial Temperature of Simulated Annealing

The classical version of simulated annealing is based on a cooling schedule. Generally, the initial temperature is set such that the acceptance ratio of bad moves is equal to a certain value χ0. In this paper, we first propose a simple algorithm to compute a temperature which is compatible with a given acceptance ratio. Then, we study the properties of the acceptance probability. It is shown that this function is convex for low temperatures and concave for high temperatures. We also provide a lower bound for the number of plateaux of a simulated annealing based on a geometric cooling schedule. Finally, many numerical experiments are reported.

Networks new economical virtual private

The idea is to reduce costs without undermining quality of service.

Between fully dynamic routing and robust stable routing

Due to the success of the Internet and the diversity of communication applications, it is becoming increasingly difficult to forecast traffic patterns. To capture the traffic variations, a flexible model where traffic belongs to a polytope was introduced in [5], [6], [4]. Using this uncertainty model, it is possible to compute a robust stable routing which is valid for any traffic matrix inside the polytope. It is also theoretically possible but practically difficult to consider a fully dynamic strategy where routing depends on the current traffic matrix. We will propose a strategy that can be seen as a compromise between robust routing and dynamic routing. It consists in partitioning the uncertainty set into some subsets and considering a robust routing for each subset. A theoretical study of this problem is provided in this paper.

Finding Failure-Disjoint Paths for Path Diversity Protection in Communication Networks

In the paper we consider a flow problem closely related to path diversity protection in communication networks. Given a weighted directed graph where some arcs are subject to failures while others are resilient, we aim at computing a shortest pair of failure-disjoint paths. If a resilient arc is used by both paths, its cost is counted only once. We present an original polynomial-time algorithm for solving the problem.

Robust routing and optimal partitioning of a traffic demand polytope

In this paper we consider the problem of optimal partitioning of a traffic demand polytope using a hyperplane. In our model all possible demand matrices belong to a polytope. The polytope can be divided into parts, and different routing schemes can be applied while dealing with traffic matrices from different parts of the polytope. We consider three basic models: Robust-Routing, No-Sharing and Dynamic-Routing. We apply two different partitioning strategies depending on whether the reservation vectors on opposite sides of the hyperplane are required to be identical, or allowed to differ. We provide efficient algorithms that solve these problems. Moreover, we prove polynomiality of some of the considered cases. Finally, we present numerical results proving the applicability of the introduced algorithms and showing differences between the routing strategies.

Efficient algorithms for the maximum concurrent flow problem

In this article, we propose a generic decomposition scheme for the maximum concurrent flow problem. This decomposition scheme encompasses many models, including, among many others, the classical path formulation and the less studied tree formulation, where the flows of commodities sharing a same source vertex are routed on a set of trees. The pricing problem for this generic model is based on shortest-path computations. We show that the tree-based linear programming formulation can be solved much more quickly than the path or the aggregated arc-flow formulation. Some other decomposition schemes can lead to even faster resolution times. Finally, an efficient strongly polynomial-time combinatorial algorithm is proposed for the single-source case.

A constraint generation algorithm for large scale linear programs using multiple-points separation

In order to solve linear programs with a large number of constraints, constraint generation techniques are often used. In these algorithms, a relaxation of the formulation containing only a subset of the constraints is first solved. Then a separation procedure is called which adds to the relaxation any inequality of the formulation that is violated by the current solution. The process is iterated until no violated inequality can be found. In this paper, we present a separation procedure that uses several points to generate violated constraints. The complexity of this separation procedure and of some related problems is studied. Also, preliminary computational results about the advantages of using multiple-points separation procedures over traditional separation procedures are given for random linear programs and survivable network design. They illustrate that, for some specific families of linear programs, multiple-points separation can be computationally effective.

A new model for multicommodity flow problems, and a strongly polynomial algorithm for single-source Maximum Concurrent Flow

In this paper, a new decomposition approach is proposed to solve large size instances of Multicommodity Flow problems. Instead of generating paths, we generate trees in a convenient way. Numerical results show that the new approach is much more efficient than the classical paths generation approach. Moreover, we propose a combinatorial polynomial-time algorithm to solve the maximum concurrent flow problem (MCF) in the single-source case.

Cables network design optimization for the Fiber To The Home

Optimization of Fiber To The Home networks is a challenging issue for telecommunications operators. This work focuses on the cables network design problem, taking into account cable separation techniques. An integer linear programming model is proposed, along with several enhancements including valid inequalities. Computational experiments are performed on real-life instances considering operators engineering rules.