Index-shuffle graphs

Abstract

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 /spl Omega/(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 /spl Omega/(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 /spl Omega/(log N), and only if the entire local data set of every processor is allowed to circulate through the network.