On the Size of Permutation Networks and Consequences for Efficient Simulation of Hypercube Algorithms on Bounded-Degree Networks
KLASING, Ralf
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
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Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
KLASING, Ralf
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
< Réduire
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Langue
en
Article de revue
Ce document a été publié dans
SIAM Journal on Discrete Mathematics. 2009, vol. 23, n° 3, p. 1612--1645
Society for Industrial and Applied Mathematics
Résumé en anglais
The sizes of permutation networks and planar permutation networks for special sets of permutations are investigated. Several asymptotically optimal estimations for distinct subsets of the set of all permutations are ...Lire la suite >
The sizes of permutation networks and planar permutation networks for special sets of permutations are investigated. Several asymptotically optimal estimations for distinct subsets of the set of all permutations are established here. The two main results are: (i) an asymptotically optimal switching network of size O(N log log N) for shifts of power 2. (ii) an asymptotically optimal planar permutation network of size Θ(N 2 • (log log N/ log N) 2) for shifts of power 2. A consequence of our results is the construction of a 4-degree network which can simulate each communication step of any hypercube algorithm using edges from at most a constant number of different dimensions in one communication step in O(log log N) communication steps. An essential improvement of gossiping in vertex-disjoint path mode in bounded-degree networks follows.< Réduire
Mots clés en anglais
Network design and communication
Communication networks
Permutation networks
Switching networks
Parallel algorithms AMS subject classifications. 68M07
68M10
90B18
94C15
Project ANR
Algorithm Design and Analysis for Implicitly and Incompletely Defined Interaction Networks - ANR-07-BLAN-0322
Origine
Importé de halUnités de recherche