Pascal Berthomé

Revisiting parametric multi-terminal problems: Maximum flows, minimum cuts and cut-tree computations

Given an undirected network, the multi-terminal network flows analysis consists in determining the all pairs maximum flow values. In this paper, we consider an undirected network in which some edge capacities are allowed to vary and we analyze the impact of such variations on the all pairs maximum flow values. We first provide an efficient algorithm for the single parametric capacity case, and then propose a generalization to the case of multiple parametric capacities. Moreover, we provide a study on Gomory-Hu cut-tree relationships.

Sorting-based selection algorithms for hypercubic networks

Abstract. This paper presents several deterministic algorithms for selecting the k th largest record from a set of n records on any n -node hypercubic network. All of the algorithms are based on the selection algorithm of Cole and Yap, as well as on various sorting algorithms for hypercubic networks. Our fastest algorithm runs in O( lg n lg *n) time, very nearly matching the trivial

Optical Interconnections and Parallel Processing: Trends at the Interface

\Omega(\lg n)

Periodic Gossiping in Commuted Networks

lower bound. Previously, the best upper bound known for selection was O( lg n lg lg n) . A key subroutine in our O( lg n lg*n) time selection algorithm is a sparse version of the Sharesort algorithm that sorts n records using p processors,

THE EULERIAN STRETCH OF A NETWORK TOPOLOGY AND THE ENDING GUARANTEE OF A CONVERGENCE ROUTING

p\geq n

Generalized Parametric Multi-terminal Flows Problem

, in O( lg n ( lg lg p - lg lg (p/n) )2) time.

Communication Issues in Parallel Systems with Optical Interconnections

From the Publisher: Optical media are now widely used in telecommunication networks and the evolution of optical and optoelectronic technologies tends to show that their wide range of techniques could be successfully introduced in shorter distance interconnection systems. This book bridges the existing gap between research in optical interconnects and research in high performance computing and communication systems, of which parallel processing is just an example. It also provides a more comprehensive understanding of the advantages and limitations of optics as applied to high-speed communications. The book will be a vital resource for researchers and graduate students of optical interconnects, computer architectures and high-performance computing and communication systems who wish to understand the trends in the newest technologies, models and communication issues in the field.

Computation of chromatic polynomials using triangulations and clique trees

Abstract In this paper we deal with global communication schemes such as broadcasting or multicasting, in a packet (sub)network in which each node participates in the same distributed application. We want the communication scheme to be performed periodically as often as possible and with some bandwidth guarantee. Such periodicity properties are needed, for example, by multimedia and grid computation applications. We consider commuted switches in the network, i.e., each outgoing link of the switch is assigned to at most one incoming link. Each switch avoids intermediate buffering. Given a network G and a global communication scheme S, an algorithm performing S in G consists in commuting each switch and in specifying to each emitting node the infinite sequence of steps at which it will send a message. The period of this algorithm is the greatest number of steps between two messages emitted by a node. The window of the algorithm is the maximal number of steps needed by a message to reach its destination(s). We first give a general definition of the model of network we consider and of the global communication schemes we study, i.e., the many-to-all scheme where many nodes have one message to send to all the other ones. One well-known case of the many-to-all scheme we especially focus on is gossiping. We present a general way of periodically performing these communication schemes, by covering the graph by substructures called octopuses. Then we show that optimizing the period and the windoware two different problems.We end by giving some examples of applications in the torus network.

THE COMPLEXITY OF THE MAXIMAL REQUESTS SATISFACTION PROBLEM IN MULTIPOINT COMMUNICATION

In this paper, we focus on convergence packet routing techniques in an all-optical network, obtained from an Eulerian routing in the digraph modeling the target network. Given an Eulerian circuit in a digraph G, we deal with the maximal number of arcs that a packet has to follow on from its origin to its destination (we talk about the ending guarantee of the routing). We consider the Eulerian diameter of G as defined by , where Eul(G) is the set of all the Eulerian circuits in G. After giving a preliminary result about the complexity of finding ℰ(G) for any digraph G, we give some lower and upper bounds of this parameter. The main part of the paper is devoted to the description of a combinatorial design of various network topologies having good Eulerian diameters.

Detecting flows congesting a target network link

Given an undirected edge-weighted n-nodes network in which a single edge-capacity is allowed to vary, Elmaghraby studied the sensitivity analysis of the multi-terminal network flows. The procedure he proposed requires the computation of as many Gomory-Hu cut trees as the number of critical capacities of the edge, leading to a pseudo-polynomial algorithm.