
Accession Number : ADA195168
Title : Optimal Simulations by Butterfly Networks: Extended Abstract,
Corporate Author : MASSACHUSETTS INST OF TECH CAMBRIDGE
Personal Author(s) : Bhatt, Sandeep N ; Chung, Fan R ; Hong, JiaWei ; Leighton, F T ; Rosenberg, Arnold
PDF Url : ADA195168
Report Date : Nov 1987
Pagination or Media Count : 13
Abstract : We investigate the power of the Butterfly network (which is the FFT network with inputs and outputs identified) relative to other proposed multicomputer interconnection networks, by considering how efficiently the Butterfly can simulate the other networks: Formally we ask, How efficiently can one embed the graph underlying the other network in the graph underlying the Butterfly? We measure the efficiency of an embedding of a graph G in a graph H in terms of: the dilation, or, the maximum amount that any edge of G is 'stretched' by the embedding; the expansion, or, the ratio of the number of vertices of H to the number of vertices of G. We present three simulations that are optimal, to within constant factors: (1) Any complete binary tree can be embedded in a Butterfly graph, with simultaneous dilation O(1) and expansion O(1). (2) The nvertex Xtree can be embedded in a Butterfly graph with simultaneous dilation O(log log n) and expansion O(1); no embedding has better dilation, independent of expansion. (3) Any embedding of the n x n mesh in the Butterfly graph must have dilation (log n), independent of expansion; any embedding of the mesh in the Butterfly graph achieves this dilation. Thus, we have simulations of completebinarytree machines, Xtree machines, and mesh computers on Butterfly machines, that are optimal in resource utilization (expansion) and delay (dilation), to within constant factors.
Descriptors : *CIRCUIT INTERCONNECTIONS, *COMPUTERS, *EMBEDDING, *GRAPHS, *MESH, *NETWORKS, ABSTRACTS, EXPANSION, OPTIMIZATION, RATIOS, RESOURCES, SIMULATION, UTILIZATION
Subject Categories : Command, Control and Communications Systems
Distribution Statement : APPROVED FOR PUBLIC RELEASE