Showing papers by "Laurent Viennot published in 2008"

On the locality of distributed sparse spanner construction

Abstract: The paper presents a deterministic distributed algorithm that, given k ≥ 1, constructs in k rounds a (2k-1,0)-spanner of O(k n1+1/k) edges for every n-node unweighted graph. (If n is not available to the nodes, then our algorithm executes in 3k-2 rounds, and still returns a (2k-1,0)-spanner with O(k n1+1/k) edges.) Previous distributed solutions achieving such optimal stretch-size trade-off either make use of randomization providing performance guarantees in expectation only, or perform in logΩ(1)n rounds, and all require a priori knowledge of n. Based on this algorithm, we propose a second deterministic distributed algorithm that, for every e > 0, constructs a (1+e,2)-spanner of O(e-1 n3/2) edges in O(e-1) rounds, without any prior knowledge on the graph.Our algorithms are complemented with lower bounds, which hold even under the assumption that n is known to the nodes. It is shown that any (randomized) distributed algorithm requires k rounds in expectation to compute a (2k-1,0)-spanner of o(n1+1/(k-1)) edges for k ∈ {2,3,5}. It is also shown that for every k>1, any (randomized) distributed algorithm that constructs a spanner with fewer than n1+1/k + e edges in at most ne expected rounds must stretch some distances by an additive factor of nΩ(e). In other words, while additive stretched spanners with O(n1+1/k) edges may exist, e.g., for k=2,3, they cannot be computed distributively in a sub-polynomial number of rounds in expectation.

Achievable catalog size in peer-to-peer video-on-demand systems

Abstract: We analyze a system where n set-top boxes with same upload and storage capacities collaborate to serve r videos simultaneously (a typical value is r = n). We give upper and lower bounds on the catalog size of the system, i.e. the maximal number of distinct videos that can be stored in such a system so that any demand of at most r videos can be served. Besides r/n, the catalog size is constrained by the storage capacity, the upload capacity, and the maximum number of simultaneous connections a box can open. We show that the achievable catalog size drastically increases when the upload capacity of the boxes becomes strictly greater than the playback rate of videos.

Scalable Distributed Video-on-Demand: Theoretical Bounds and Practical Algorithms

Abstract: We analyze a distributed system where n nodes called boxes store a large set of videos and collaborate to serve simultaneously n videos or less We explore under which conditions such a system can be scalable while serving any sequence of demands We model this problem through a combination of two algorithms: a video allocation algorithm and a connection scheduling algorithm The latter plays against an adversary that incrementally proposes video requests

Construction locale de sous-graphes couvrants peu denses

Abstract: Nous présentons un algorithme distribué déterministe qui calcule pour tout graphe simple non pondéré, un sous-graphe couvrant (spanner) avec O(kn1+1/k) arêtes et un facteur d’étirement (2k−1,0), n étant le nombre de sommets du graphe et k un paramètre entier strictement positif. Si n est inconnu l’algorithme termine en temps 3k−2, sinon il termine en temps k. En se basant sur cet algorithme pour k = 2, nous construisons de façon déterministe un sous-graphe couvrant avec O(ε−2n3/2) arêtes et un facteur d’étirement (1+ε,2) en O(ε−1) temps, ε > 0 est un paramètre arbitrairement petit.