Efficient routing and message bounds for optimal parallel algorithms

The cost of interprocessor communication has a substantial impact on execution time when implementing parallel algorithms on physical parallel computers. We study these implementation costs, examining the number of inter-processor messages, the cost of routing these messages on various architectures, and the number of communication phases. We provide an improved direct routing algorithm for realizing h-relations on crossbar networks. We also introduce a round-robin message-delivery algorithm which reduces the number of times a communication lint is established between a pair of processors (by delivering all messages of that phase for the pair in order without interruption) We summarize criteria sufficient for a parallel algorithm to be implemented optimally on several common networks. We also describe a log n-phase optimal parallel list-ranking algorithm