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

The mv-decomposition: definition and application to the distance-2 broadcast problem in multi-hops radio networks

Abstract We present a new tool called the "mv-decomposition", and we describe some interesting algorithmic properties about it. We propose an algorithm with a complexity of O(m) to build a mv-decomposition for each bipartite graph. We use this mv-decomposition to propose a solution to the distance-2 broadcast problem in a synchronous multi-hops radio networks where adjacent transmissions are subject to interferences. More precisely, we propose two algorithms of resolution: the first one guarantees a complete distance-2 broadcast scheme using O((log n) 2 ) slots for a time complexity of O(m(log n) 2 ), while the second builds a solution with a minimal number of transmissions for a time complexity of O(m)

Computing Maximum Stable Set for Distance-Hereditary Graphs

Open ArchiveInternational audienceIn this note, we provide a new and simple algorithm to compute maximum stable sets for distance-hereditary graphs. It corrects the algorithm presented by Hammer and Maffray [Discrete Appl. Math. 27 (1990) 85–99], but remains within the general greedy scheme that was suggested by Hammer and Maffray (1990)

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]

On the List Colouring Problem

International audienc

The MV-Decomposition: Definition and Application to the Distance-2 Broadcast Problem in Multi-Hops Radio Networks

International audienceWe present a new tool called the "mv- decomposition", and we describe some interesting algorithmic properties about it. We propose an algorithm with a complexity of $O(m)$ to build a mv-decomposition for each bipartite graph. We use this mv-decomposition to propose a solution to the distance-2 broadcast problem in a synchronous multi-hops radio networks where adjacent transmissions are subject to interferences. More precisely, we propose two algorithms of resolution: the first one guarantees a complete distance-2 broadcast scheme using $O((log n )2)$ slots for a time complexity of $O (m (log n)2)$, while the second builds a solution with a minimal number of transmissions for a time complexity of $O(m)$