Divide-and-Conquer Algorithms on Two-Dimensional Meshes

The Reflecting and Growing mappings have been proposed to map parallel divide-and-conquer algorithms onto two-dimensional meshes. The performance properties of these mappings have been analysed under the assumption that the parallel algorithm is initiated always at the same fixed node of the mesh. In this scenario, the Reflecting mapping is optimal for meshes with wormhole routing and the Growing mapping is very close to the optimal for meshes with store-and-forward routing. In this paper we consider a more general scenario in which the parallel divide-and-conquer algorithm can be started from an arbitrary node of the mesh. It is shown that, in this new scenario, while the Reflecting mapping is still optimal for a wormhole mesh, the performance of the Growing mapping in store-and-forward meshes decreases very quickly when the mesh size increases. An alternative approach is proposed which, besides being simpler than both the Reflecting and Growing mappings, is also optimal for wormhole ..