BERMOND , Jean-Claude

International audience

The idea of editing a special issue on Interconnection Networks came from discussions with many other researchers, particularly during specialized workshops. This idea was enthusiastically supported by P.L. Hammer who proposed that it could be a special issue of Discrete Applied Mathematics which we have called DAMIN. The aim was to gather...

State-of-the-art on traffic grooming with a design theory approach

We address the problem of traffic grooming in WDM rings with all-to-all uniform unitary traffic. We want to minimize the total number of SONET add-drop multiplexers (ADMs) required. We show that this problem corresponds to a partition of the edges of the complete graph into subgraphs, where each subgraph has at most C edges (where C is the...

This paper considers the question of the in uence of a coalition of vertices, seeking to gain control (or majority) in local neighborhoods in a general graph. Say that a vertex v is controlled by the coalition M if the majority of its neighbors are from M. We ask how many vertices (as a function of jMj) can M control in this fashion. Upper and...

We study the minimization of ADMs (Add-Drop Multiplexers) in optical WDM bidirectional rings considering symmetric shortest path routing and all-to-all unitary requests. We precisely formulate the problem in terms of graph decompositions, and state a general lower bound for all the values of the grooming factor $C$ and $N$, the size of the...

Broadcasting is an information dissemination process in which a message is to be sent from a single originator to all members of a network by placing calls over the communication lines of a network. To broadcast time of a vertex is the minimim number ot time units required to complete broadcasting from this vertex. Several previous papers have...

In this paper we give a survey of the known properties of the Bruijn and Kautz networks showing that their behavior is as good as the hypercube's. As they have the advantage of connecting considerably more processors, they are good competitors for the hypercube and might constitute the next generation of parallel architectures.

Broadcasting is an information dissemination process in which a message is to be sent from a single originator to all members of a network by placing calls over the communication lines of the network. This is to be completed as quickly as possible subject to the constraints that each call involves only two vertices, each call requires one unit...

International audience

Let P be a family of dipaths. The load of an arc is the number of dipaths containing this arc. Let (G,P) be the maximum of the load of all the arcs and let w(G,P) be the minimum number of wavelengths (colors) needed to color the family of dipathsP in such a way that two dipaths with the same wavelength are arc-disjoint. Let G be a DAG (Directed...

We consider traffic grooming in WDM unidirectional rings with all-to-all uniform unitary traffic. We determine the minimum number of SONET/SDH add-drop multiplexers (ADMs) required when the grooming ratio is 3. In fact, using tools of design theory, we solve the equivalent edge partitioning problem: find a partition of the edges of the complete...

International audience

International audience

International audience

This article deals with the problem of minimizing the transmission delay in Illiac-type interconnection networks for parallel or distributed architectures or in local area networks. A double-loop networks (also known as circulant) G (n,h) consist of a loop of n vertices where each vertex i is also joined by chords to the vertices i +- h mod n....

International audience

La théorie des graphes constitue un domaine des mathématiques qui s'est développé au sein de disciplines diverses telles que la chimie (modélisation de structures), la biologie (génome), les sciences sociales (modélisation des relations) et le transport (réseaux routiers, électriques, etc.). Le cycle eulérien et le cycle hamiltonien Réseaux...

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We study the problem of gathering information from the nodes of a radio network into a central node. We model the network of possible transmissions by a graph and consider a binary model of interference in which two transmissions interfere if the distance in the graph from the sender of one transmission to the receiver of the other is $d_I$ or...

International audience

We study the problem of gathering information from the nodes of a radio network into a central node. We model the network of possible transmissions by a graph and consider a binary model of interference in which two transmissions interfere if the distance in the graph from the sender of one transmission to the receiver of the other is $d_I$ or...

International audience

International audience

We study the problem of gathering information from the nodes of a radio network into a central destination node. A transmission can be received by a node if it is sent from a distance of at most d T and there is no interference from other transmissions. One transmission interferes with the reception of another transmission if the sender of the...