带集群的多处理器最大加速的最优下界

L. Lundberg, H. Lennerstad
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引用次数: 14

摘要

我们考虑一个理想的多处理器系统,它有q个处理器和一个没有开销的集中式调度程序,它从一个公共池中选择进程,允许进程的动态重新定位。由n个进程组成的并行程序P在该系统上执行,当所有进程完成时终止。由于同步,进程可能在等待其他进程中的事件时被阻塞。并行程序使用进程到处理器的一些调度来执行,导致加速/spl σ /。然后我们考虑一个理想的多处理器,它有k个集群,每个集群包含u个处理器。在此系统中,进程不能在集群之间重新定位。找到一个能够带来最大加速的时间表是np困难的。在这里,我们给出了程序P的最大加速的最优下界的公式,作为q, n, /spl sigma/, k和u的函数。我们还给出了当进程数(n)未知时的最优下界的公式。利用这些结果,我们能够决定某个时间表是否接近最佳,或者是否值得寻找其他时间表。这是通过评估特定程序的特定时间表的加速来证明的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An optimal lower bound on the maximum speedup in multiprocessors with clusters
We consider an ideal multiprocessor system with q processors and a centralized scheduler without overhead that selects processes from one common pool, permitting dynamic relocation of processes. A parallel program P consisting of n processes is executed on this system and terminates when all processes are completed. Due to synchronizations, processes may be blocked while waiting for events in other processes. The parallel program is executed using some schedule of processes to processors, resulting in a speedup /spl sigma/. We then consider an ideal multiprocessor with k clusters containing u processors each. In this system processes may not be relocated between clusters. Finding a schedule which results in maximum speedup is NP-hard. Here, we present a formula for the optimal lower bound on the maximum speedup for program P, as a function of q, n, /spl sigma/, k and u. We also present a formula for the optimal lower bound when the number of processes (n) is unknown. Using these results we are able to decide if a certain schedule is close to optimal or if it is worth-while to look for other schedules. This is demonstrated by evaluating the speedup of a specific schedule of a particular program.<>
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