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 of these mappings has been previously analyzed under the assumption that the parallel algorithm is initiated always at the same fixed node of the mesh. In such 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 at an arbitrary node of the mesh. We propose and approach that is simpler than both the Reflecting and Growing mappings, is optimal for wormhole meshes and better than the Growing mapping for store-and-forward meshes.