Efficient Total-Exchange in Wormhole-Routed Toroidal Cubes

The total-exchange is one of the most dense communication patterns and is at the heart of numerous applications and programming models in parallel computing. In this paper we present a simple randomized algorithm to efficiently schedule the total-exchange on a toroidal mesh with wormhole switching. This algorithm is based on an important property of the wormhole networks that reach high performance under uniform traffic using adaptive routing. The experimental results, conducted on a 256 nodes bi-dimensional torus, show that this algorithm reaches a very high level of performance, around 90% of the optimal bound, and is more efficient than other algorithms presented in the literature.