Optimal Schedule for All-to-All Personalized Communication in Multiprocessor Systems.
ACM Transactions on Parallel Computing(2019)
摘要
In this article, we address the problem of finding an optimal schedule for all-to-all personalized message communication among the processors in a multiprocessor system where every processor has a unique message for every other processor. When there are n processors and ⌊n/2⌋ parallel databus or channels for message communications, there exist algorithms that require O(n2) time for assigning the databus/channels to the processor-pairs to obtain a schedule with minimum number of time slots. However, in recent massively parallel processing systems with a huge number of processors, the number k of available databus/channels is usually much smaller than ⌊n/2⌋. Thus, in each round of communication, only k processor-pairs (k < ⌊n/2⌋) can exchange their messages in parallel. We address this general case of all-to-all personalized communication and present a new technique for scheduling the channels among processor-pairs where only k < ⌊n/2⌋ databus/channels are available. We show that the proposed technique is optimal for all values of n other than 2k < n < 3k. For 2k < n < 3k, we show that the required number of rounds may be more than the lower bound of ⌈n/(n−1)2k⌉ by at most 11%, and proving the optimality of our technique remains as an open problem in this case.
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关键词
Multiprocessor systems,all-to-all personalized communication,interconnection-networks,message transfer,multi-port processors,optimal-schedule
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