Parallel implementation of divide-and-conquer algorithms on binary de Bruijn networks

Abstract

Studies the problem of parallel implementation of divide-and-conquer algorithms on binary de Bruijn network using a temporal binomial tree (rather than the usual binary tree) computation structure. Two cases of message volumes are considered: (i) uniform, and (ii) logarithmically decreasing (increasing) weights. A single mapping is proposed for both cases. It has average extra dilation 1 and is communication link contention-free. A lower bound for the total extra dilation of any mapping from uniform-weighted binomial tree to an arbitrary degree-4 network is also developed to show that the mapping is asymptotically optimal with respective to the average extra dilation. The implementation is well suited to a binary de Bruijn network with a wormhole or circuit switching communication scheme.<>