Parallel Divide and Conquer on Meshes

We address the problem of mapping divide-and-conquer programs to mesh connected multicomputers with wormhole or store-and-forward routing. We propose the binomial tree as an eecient model of parallel divide-and-conquer and present two mappings of the binomial tree to the 2D mesh. Our mappings exploit regularity in the communication structure of the divide-and-conquer computation and are also sensitive to the underlying ow control scheme of the target architecture. We evaluate these mappings using new metrics which are extensions of the classical notions of dilation and contention. We introduce the notion of communication slowdown as a measure of the total communication overhead incurred by a parallel computation. We conclude that signiicant performance gains can be realized when the mapping is sensitive to the ow control scheme of the target architecture.