Sacha Varone

An Ant Algorithm for the Steiner Tree Problem in Graphs

The Steiner Tree Problem (STP) in graphs is a well-known NP-hard problem. It has regained attention due to the introduction of new telecommunication technologies, since it is the mathematical structure behind multi-cast communications. The goal of this paper is to design an ant algorithm (called ANT-STP) for the STP in graphs which is better than TM, which is a greedy constructive method for the STP proposed in [34]. We derive ANT-STP from TM as follows: each ant is a constructive heuristic close to TM, but the population of ants can collaborate by exchanging information by the use of the trail systems. In addition, the decision rule used by each individual ant is different from the decision rule used in TM. We compare TM and ANT-STP on a set of benchmark problems of the OR-Library.

The Metric Cutpoint Partition Problem

Let G = (V, E,w) be a graph with vertex and edge sets V and E, respectively, and w: E →

A constructive algorithm for realizing a distance matrix

\mathbb{R}^{+}

The Metric Bridge Partition Problem: Partitioning of a Metric Space into Two Subspaces Linked by an Edge in Any Optimal Realization

a function which assigns a positive weight or length to each edge of G. G is called a realization of a finite metric space (M, d), with M = {1, ..., n} if and only if {1, ..., n} ⊆ V and d(i, j) is equal to the length of the shortest chain linking i and j in G ∀i, j = 1, ..., n. A realization G of (M, d), is called optimal if the sum of its weights is minimal among all the realizations of (M, d). A cutpoint in a graph G is a vertex whose removal strictly increases the number of connected components of G. The Metric Cutpoint Partition Problem is to determine if a finite metric space (M, d) has an optimal realization containing a cutpoint. We prove in this paper that this problem is polynomially solvable. We also describe an algorithm that constructs an optimal realization of (M, d) from optimal realizations of subspaces that do not contain any cutpoint.

Service design needs for luxury e-commerce: An empirical study

The natural metric of a weighted graph is the length of the shortest paths between all pairs of vertices. The investigated problem consists in a representation of a given metric by a graph, such that the total length of the graph is minimized. For that purpose, we give a constructive algorithm based on a technique of reduction, fusion and deletion. We then show some results on a set of various distance matrices whose optimal realization is known.

Three tabu search methods for the MI-FAP applied to 802.11 networks

Let G = (V,E,w) be a graph with vertex and edge sets V and E, respectively, and w:E → R + a function which assigns a positive weight or length to each edge of G. G is called a realization of a finite metric space (M,d), with M = { 1,...,n} if and only if { 1,...,n} ⫅ V and d(i,j) is equal to the length of the shortest chain linking i and j in G ∀ i,j = 1,...,n. A realization G of (M,d), is said optimal if the sum of its weights is minimal among all the realizations of (M,d). Consider a partition of M into two nonempty subsets K and L, and let e be an edge in a realization G of (M,d); we say that e is a bridge linking K with L if e belongs to all chains in G linking a vertex of K with a vertex of L. The Metric Bridge Partition Problem is to determine if the elements of a finite metric space (M,d) can be partitioned into two nonempty subsets K and L such that all optimal realizations of (M,d) contain a bridge linking K with L. We prove in this paper that this problem is polynomially solvable. We also describe an algorithm that constructs an optimal realization of (M,d) from optimal realizations of (K,d|K) and (L,d|L).

Collaborative channel affectation vs greedy method for 802.11 b/g networks

Nowadays, we are just in the launching phase of luxury e-business, it is not clear whether it should be served with a luxury service from a physical shop, or not. Do consumers especially wish a pre- and after-sales service which is taken in charge by a physical shop while buying on the official luxury website? After the opinion of luxury bloggers, we do know that there is a need for luxury service offer which comes with luxury e-commerce in general and specifically for pre- and after-sales services[1]. Our results are based on 168 questionnaires from international luxury e-shoppers. They show clearly that luxury consumers, who buy luxury goods via internet, do need a physical shop. Additionally this physical shop has to assume all pre- and after-sales issue. So, luxury e-commerce does not replace the physical independent wholesaler network, but has to be integrated in a complementary strategy with it.

Real-Time Ride-Sharing Substitution Service in Multi-modal Public Transport Using Buckets

Wireless LAN using IEEE 802.11 networks are now widely deployed at home by residential users or in hot spots by telecommunication operators. A hot spot is a place where a set of access points (APs) are located nearby each other and can serve many users. Since perturbations can degrade the quality of the signal, a careful channel assignment to each AP has to be done. Channel assignment of APs at hot spots, and more generally setup configuration and management, is still often done manually. In this paper, we consider a modeling that enables optimization of channel assignment with respect to the dynamic behavior of end-users. We prove our problems formulation to correspond to the Minimum Interference Frequency Assignment Problem, and hence the problem to be NP-hard. We propose and compare three different tabu search methods to solve the problem of channel assignment in 802.11 WLAN networks. The first one, called TabuObj, tackles the problem using directly the objective function associated with the model. The second one, called TabuApproxObj, uses a simplified and approximate objective function in order to visit more solutions during the same amount of time, i.e. to be quicker than TabuObj. The third one, called TabuLevel, is even more quicker and is based on the following philosophy: under time constraints, it could be judicious to explore very quickly lots of solutions, rather than spending much computation time for the evaluation of each solution, and hence only considering a few solutions. Those three methods are then compared based on time constraints and on the quality of their solutions.

Carpooling as Complement to Multi-modal Transportation

This article shows the added-value of a collaborative channel affectation, called RME for resource management engine, in a hotspot. It shows that if access points are configured sequentially by choosing at each access point the best current channel and never change afterwards, then the collaborative channel affectation gives a higher quality of service in terms of throughput. As there is even some benefits from this collaborative channel affectation in a static environment, much more benefits can be expected in dynamic environments, which is the case in hotspots.

Staff Assignment Using Network Flow Techniques

We consider a mix transportation problem, which allows to combine a multi-modal public and a ride-sharing transports, in a dynamic environment. The main idea of our approach consists in labelling interesting nodes of a geographical map with information about either riders or drivers, in so-called buckets. Based on the information contained in these buckets, we compute admissible ride-sharing possibilities. To restrict the needed amount of memory, among the different stops along a public transportation path, we only consider the transshipment nodes, where travellers have to make a change between two modes. Each of those stops are potential pick-up or drop-off stops for ride-sharing. We consider a drivers’ maximal waiting time, as well as the maximal driving detour time depending on the actual drive. Each new drive activates a search for new ride-sharing of existing riders. Each new ride activates another process which searches for potential drivers. Among all admissible ride-sharing possibilities, only those which best improve the earliest arrival time are selected. We provide numerical results using real road network of the Lorraine region (FR) and real data provided by a local company. Our numerical experiment shows a running time of a few seconds, suitable for a new real-time transportation application.