Parallel algorithms on the rotation-exchange network-a trivalent variant of the star graph

Abstract

We investigate a trivalent Cayley graph, which we call the rotation-exchange (RE) network, and present communication algorithms to perform one-to-one routing, single-node broadcasting, multinode broadcasting, and total exchange in it. The RE network can be viewed as a stargraph counterpart to the hypercubic shuffle-exchange network, with the important difference that the RE network is regular and symmetric. We show that RE networks can efficiently embed and emulate star graphs, meshes, hypercubes, cube connected cycles (CCC), pancake graphs, bubble-sort graphs, complete transposition graphs, and the shuffle-exchange permutation graphs. We also show that the performance of RE networks can be significantly improved for a variety of applications if the transmission rate of on-chip links is considerably higher than that of off-chip links.