Approximable 1-Turn Routing Problems in All-Optical Mesh Networks

In all-optical networks, several communications can be transmitted through the same fiber link provided that they use different wavelengths. The MINIMUM ALL-OPTICAL ROUTING problem (given a list of pairs of nodes standing for as many point to point communication requests, assign to each request a route along with a wavelength so as to minimize the overall number of assigned wavelengths) has been paid a lot of attention and is known to be N P–hard. Rings, trees and meshes have thus been investigated as specific networks, but leading to just as many N P–hard problems. This paper investigates 1-turn routings in meshes (paths are allowed one turn only). We first show the MINIMUM LOAD 1-TURN ROUTING problem to be N P–hard but 2-APX (more generally, the MINIMUM LOAD k-CHOICES ROUTING problem is N P–hard but k-APX), then that the MINIMUM 1-TURN PATHS COLOURING problem is 4-APX (more generally, any d-segmentable routing of load L in a hypermesh of dimension d can be coloured with 2d(L−1)+1 colours at most). >From there, we prove the MINIMUM ALL-OPTICAL 1-TURN ROUTING problem to be APX

Les machines : architecture des ordinateurs - d'une introduction historique à la définition d'une machine virtuelle universelle -

Cet article est une présentation de ce qu'on appelle communément l'architecture des ordinateurs en Informatique. Il est destiné aux étu-diants de niveau Licence ou Master en Informatique, notamment à ceux préparant un CAPES d'informatique, comme aux enseignants du secondaire qui souhaitent accompagner l'apparition de la discipline Informatique au lycée. Il suit un plan en 5 parties :-La genèse des ordinateurs où l'on introduit progressivement et en suivant la voie historique les étapes qui ont conduit aux fon-dements de l'architecture que l'on connaît actuellement-L'architecture de base des ordinateurs en exposant les grands principes communs à toutes les réalisations-La présentation d'un Ordinateur Réduit Facile Évolutif Universel (que nous appelons ORFEU) illustrant ce type d'architecture et son langage d'assemblage (LAMOR). Cet ordinateur et ce lan-gage pouvant également servir de base à l'élaboration de séances d'enseignement.-Quelques extensions facilitant la programmation d'un ordinateur de base-Les architectures évoluées du processeur et des mémoires Il est suivi d'une brève conclusion et de quelques annexes Table des matières 1 La genèse 4

Choosability of bipartite graphs with maximum degree DeltaDelta

Let G=(V(G), E(G)) be a graph. A list assignment is an assignment of a set L(v) of integers to every vertex v of G. An L-colouring is an application C from V(G) into the set of integers such that C(v)L(v) for all v V(G) and C(u)C(v) if u and v are joined by an edge. A (k,k')-list assignment of a bipartite graph G with bipartition (A,B) is a list assignment L such that |L(v)|= k if vA and |L(v)|= k' if vB. A bipartite graph is (k,k')-choosable if it admits an L-colouring for every (k.k')-list assignment L. In this paper, we study the (k,k')-choosability of graphs. Alon and Tarsi proved in an algebraic and non-constructive way, that every bipartite graph with maximum degree is (/2 +1, /2 +1)-choosable. In this paper, we give an alternative and constructive proof to this result. We conjecture that this result is sharp (i.e. there is a bipartite graph with maximum degree that is not (/2 , /2 +1)-choosable) and prove it for 5. Moreover, for a fixed , we show that given a bipartite graph with maximum degree and a (/2 , /2)+1)-list assignment L, it is NP-complete to decide if G is L-colourable. At last, we give upper bounds for the minimum size n_3() of a non (3,3)-choosable bipartite graph with maximum degree : n_3(5)846 and n_3(6)128

Problèmes algorithmiques dans les réseaux tout-optique

MONTPELLIER-BU Sciences (341722106) / SudocSudocFranceF

On the List Colouring Problem

International audienc

Multicast routing in WDM networks without splitters

International audienceMulticasting in WDM core networks is an efficient way to economize network resources for several multimedia applications. Due to their complexity and cost, multicast capable switches are rare in the proposed architectures. The paper investigates the multicast routing without splitters in directed (asymmetric) graphs. The objective is to minimize the number of used wavelengths and if there are several solutions, choose the lowest cost one. We show that the optimal solution is a set of light-trails. An efficient heuristic is proposed to minimize conflicts between the light-trails, and so to minimize the number of used wavelengths. The performance is compared to existing light-trail based heuristics. Our algorithm provides a good solution with a few wavelengths required and a low cost

An Improved Multicast Routing Algorithm in Sparse Splitting WDM Networks

International audienceIn this paper we study the multicast routing problem in all-optical WDM networks with sparse splitting capacity. This problem have been attracted a lot of attentions by the researchers worldwide due to its challenges and interest. Most of the work makes use of light-trees (or light-forests) to solve the problem. The objective focuses mainly on minimizing the network resources, e.g. the maximum number of wavelengths (the link stress), the number of wavelength channels used (the total cost), or the end-to-end delay from the source to the destinations (the delay). However, archiving multiple objectives is not trivial. For this reason, we propose a comparative study of the most known algorithms and introduce a new one which can provide a good trade-off among those three criteria. Simulation results and comparison point out that our proposal produces multicast light-forests with the lowest link stress, low total cost and a low end-to-end delay among considered algorithms. Especially, our proposal is more advantageous in dense networks, and/or with a large multicast group size in comparison to the classical algorithms

A 4-approximation for the line-column paths colouring problem in bi-directed meshes networks

We study the row-column chain coloring problem in directed meshes (each directed chain is of one out of eight possible types). The decision problem is known to be NP-complete, and an 8-approximation algorithm has been provided for the associated optimization problem [KT03]. We improve on this result by providing a 4-approximation algorithm, thus catching up with the best non directed result known to us [BCP06]