Papers by Stéphane Perennes
About the Lifespan of Peer to Peer Networks
Lecture Notes in Computer Science, 2006
Lecture Notes in Computer Science, 2000
In this paper we introduce a new class of shortest path problems, where the contribution of a lin... more In this paper we introduce a new class of shortest path problems, where the contribution of a link to the path length computation depends not only on the weight of that link but also on the weights of the links already traversed. This class of problems may be viewed as "non-Markovian". We consider a specific problem that belong to this class, which is encountered in the multimedia data transmission domain. We consider this problem under different conditions and develop algorithms. The shortest path problem in multimedia data transmission environment can be solved in O(n 2) or O(n 3) computational time.
Neighbourhood Gossiping in Hypercubes
Parallel Processing Letters, 1998
In the neighbourhood gossiping problem, each node of a network starts with a unique message and m... more In the neighbourhood gossiping problem, each node of a network starts with a unique message and must learn the messages of all of its neighbours. In this paper, we prove upper and lower bounds for neighbourhood gossiping in hypercubes under the single-port half-duplex and single-port full-duplex communication models.
Journal of Graph Theory, 2001
Let T be a symmetric directed tree, i.e., an undirected tree with each edge viewed as two opposit... more Let T be a symmetric directed tree, i.e., an undirected tree with each edge viewed as two opposite arcs. We prove that the minimum number of colors needed to color the set of all directed paths in T, so that two paths of the same color never use the same directed arc of T, is equal to the maximum number of different paths that contain the same arc of T. The proof implies a polynomial time algorithm for actually coloring the paths with the minimum number of colors. When only a subset of the directed paths is to be colored, the problem is known to be NP‐complete; we describe certain instances of the problem which can be efficiently solved. These results are applied to WDM (wavelength‐division multiplexing) routing in all‐optical networks. In particular, we solve the all‐to‐all gossiping problem in optical networks. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 183–196, 2001
IEEE Transactions on Parallel and Distributed Systems, 1996
Discrete Applied Mathematics, 1998
A generalized cycle is a digraph whose set of vertices is partitioned in several parts that are c... more A generalized cycle is a digraph whose set of vertices is partitioned in several parts that are cyclically ordered in such a way that the vertices in one part are adjacent only to vertices in the next part. The problems considered in this paper are: 1. To find generalized cycles with given maximum out-degree and diameter that have large order. 2. To find generalized cycles with small diameter for given values of their maximum out-degree and order. A bound is given for both problems. It is proved that the first bound can only be attained for small values of the diameter. We present two new families of generalized cycles that provide some solutions to these problems. These families are a generalization of the generalized de Bruijn and Kautz digraphs and the bipartite digraphs BD(N',n).
Sorting-Based Selection Algorithms for Hypercubic Networks
Algorithmica, 2000
Formulation en Coupes/Rounds pour le Routage dans les R´ eseaux Radio Maill
The minimum range assignment problem on linear ratio networks. (Extended abstract)
Given a set S of ratio stations located on a line and an integer h (1≤h≤|S|-1), the Min Assignmen... more Given a set S of ratio stations located on a line and an integer h (1≤h≤|S|-1), the Min Assignment problem is to find a range assignment of minimum power consumption provided that any pair of stations can communicate in at most h hops. Previous positive results for this problem were known only when h=|S|-1 (i.e. the unbounded case) or when the stations are equally spaced (i.e. the uniform chain). In particular, Kirousis, Kranakis, Krizanc and Pelc (1997) provided an efficient exact solution for the unbounded case and efficient approximated solutions for the uniform chain, respectively. This paper presents the first polynomial time, approximation algorithm for the Min Assignment problem. The algorithm guarantees an approximation ratio of 2 and runs in time O(hn 3 ). We also prove that, for constant h and for “well spread” instances (a broad generalization of the uniform chain case), we can find a solution in time O(hn 3 ) whose cost is at most an (1+ε(n)) factor from the optimum, whe...
Proceedings 14th International Parallel and Distributed Processing Symposium. IPDPS 2000, 2000
Traffic grooming in WDM networks with multi-layer switches
2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333)
Acyclic orientations for deadlock prevention in interconnection networks
Lecture Notes in Computer Science, 1997
Gossiping in Torus with Circuit-Switched Routing
Bar-Noy, A., JA Garay and A. Herzberg, Sharing video on demand (1) 3–30 Barriere, L., Symmetry properties of chordal rings of degree 3 (2–3) 211–232 Benczur, AA, Pushdown–reduce: an algorithm for connectivity augmentation and poset covering problems (2–3) 233–262
Gossiping in torus with wormhole-like routing
This paper deals with collective communications ondistributed-memory parallel machines. We are in... more This paper deals with collective communications ondistributed-memory parallel machines. We are interestedin the design of efficient gossiping (total exchange)algorithms on square torus of processing nodesusing wormhole-like routing mechanism. The executiontime is influenced by three factors, namely, thenumber of steps, the transmission rate and the maximumdistance to cross. We first compute the lowerbounds of the gossiping problem under these assumptions.Then, we
The notion of Shared Risk Link Groups (SRLG) captures survivability issues when a set of links of... more The notion of Shared Risk Link Groups (SRLG) captures survivability issues when a set of links of a network may fail simultaneously. The theory of survivable network design relies on basic combinatorial objects that are rather easy to compute in the classical graph models: shortest paths, minimum cuts, or pairs of disjoint paths. In the SRLG context, the optimization criterion for these objects is no longer the number of edges they use, but the number of SRLGs involved. Unfortunately, computing these combinatorial objects is NP-hard and hard to approximate with this objective in general. Nevertheless some objects can be computed in polynomial time when the SRLGs satisfy certain structural properties of locality which correspond to practical ones, namely the star property (all links affected by a given SRLG are incident to a unique node) and the span 1 property (the links affected by a given SRLG form a connected component of the network). The star property is defined in a multi-colored model where a link can be affected by several SRLGs while the span property is defined only in a mono-colored model where a link can be affected by at most one SRLG. In this paper, we extend these notions to characterize new cases in which these optimization problems can be solved in polynomial time. We also investigate the computational impact of the transformation from the multi-colored model to the mono-colored one. Experimental results are presented to validate the proposed algorithms and principles.
Lecture Notes in Computer Science, 2001
This paper addresses the natural relaxation of the path coloring problem, in which one needs to c... more This paper addresses the natural relaxation of the path coloring problem, in which one needs to color directed paths on a symmetric directed graph with a minimum number of colors, in such a way that paths using the same arc of the graph have different colors. This classic combinatorial problem finds applications in the minimization of the number of wavelengths in wavelength division multiplexing (wdm) all-optical networks.
Proceedings 11th International Parallel Processing Symposium
Gossiping is an extensively investigated information dissemination process in which each processo... more Gossiping is an extensively investigated information dissemination process in which each processor has a distinct item of information and has to collect all the items possessed by the other processors. In this paper, we provide an innovative and general lower bound technique relying on the novel notion of delay digraph of a gossiping protocol and on the use of matrix norm methods. Such a technique is very powerful and allows the determination of new and significantly improved lower bounds in many cases. In fact, we derive the first general lower bound on the gossiping time of systolic protocols, i.e., constituted by a periodic repetition of simple communication steps. In particular, given any network of n processors and any systolic period s, in the directed and the undirected half-duplex cases every s-systolic gossip protocol takes at least log(n)/ log(1/) − O(log log(n)) time steps, where is the unique solution between 0 and 1 of • p s/2 () • p s/2 () = 1, with p i () = 1 + 2 + • • • + 2i−2 for any integer i > 0. We then provide improved lower bounds in the directed and half-duplex cases for many well-known network topologies, such as Butterfly, de Bruijn and Kautz graphs. All the results are extended also to the full-duplex case. Our technique is very general, as for s → ∞ it allows the determination of improved results even for non-systolic protocols. In fact, for general networks, as a simple corollary it yields a lower bound only an O(log log(n)) additive factor
Analysis of failure correlation impact on peer-to-peer storage systems
IEEE P2P'09 - 9th International Conference on Peer-to-Peer Computing, 2009
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Papers by Stéphane Perennes