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Index-shuffle graphs

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2 Author(s)
Baumslag, M. ; Bear Stearns & Co. Inc., New York, NY, USA ; Obrenic, B.

Index-shuffle graphs are introduced as candidate interconnection networks for parallel computers. The comparative advantages of index-shuffle graphs over the standard bounded-degree “approximations” of the hypercube, namely butterfly-like and shuffle-like graphs, are demonstrated in the theoretical framework of graph embedding and network emulations. An N-node index-shuffle graph emulates: (1) an N-node shuffle-exchange graph with no slowdown, while the currently best emulations of shuffle-like graphs by hypercubes and butterflies incur a slowdown of Ω(log N); (2) its like-sized butterfly graph with a slowdown O(log log log N), while the currently best emulations of butterfly-like graphs by shuffle-like graphs incur a slowdown of Ω(log log N); (3) an N-node hypercube that executes an on-line leveled algorithm with a slowdown O(log log N) and without data circulation, while the slowdown of currently best such emulations of the hypercube by its bounded-degree shuffle-like and butterfly-like derivatives remains Ω(log N), and only if the entire local data set of every processor is allowed to circulate through the network

Published in:

Parallel and Distributed Processing, 1996., Eighth IEEE Symposium on

Date of Conference:

23-26 Oct 1996