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

Xiaoxiong Zhong, S. Rajopadhye, V. Lo
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引用次数: 6

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.<>
二进制de Bruijn网络上分治算法的并行实现
采用时间二叉树(而不是通常的二叉树)计算结构,研究了二分de Bruijn网络上分治算法的并行实现问题。考虑消息量的两种情况:(i)均匀,和(ii)对数减少(增加)权重。对于这两种情况,建议使用单个映射。它具有平均额外膨胀1,并且通信链路无争用。给出了从等权二叉树到任意4次网络的任意映射的总额外展开的下界,证明了该映射相对于平均额外展开是渐近最优的。该实现非常适合于具有虫洞或电路交换通信方案的二进制de Bruijn网络
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