Vinod G. J. Peris

University of Maryland at College Park. Department of Computer Science

A. Y. Oruc

M. Yaman Oruç

Abstract: "A theorem of Cayley states that every finite group is isomorphic to a permutation group. Based on this fact, this paper establishes that modulo addition, subtraction, multiplication, and division can be performed on a permutation network with O(log2m) inputs, O((log2m)log2log2m), cost and O(log2log2m), depth for all integers m; 1 [greater than or equal to] m [greater than or equal to] 2[superscript 24]."

Preliminary Version

Fast Modular Arithmetic on a Permutation Network

International Business Machines Corporation. Research Division

Mark S. Squillante

Vijay K. Naik

Abstract: "We consider an important tradeoff in distributed parallel processing systems between the impact of program inefficiencies toward reducing the number of processors allocated to parallel applications with increasing system loads and the performance impact of memory requirements toward larger allocations. To study this tradeoff, we formulate stochastic models of parallel program behavior, a distributed parallel processing system and the total memory overhead incurred by a program as a function of its processor allocation. A mathematical analysis of the models is developed, which can include the effects of contention for shared resources caused by paging activity. We conduct a detailed analysis of actual large-scale scientific applications and use these results to parameterize our models. Our results show that memory overhead resulting from processor allocation decisions can have a significant effect on system performance in distributed parallel environments. Thus, our analysis strongly suggests that memory considerations must be incorporated in the resource allocation policies for parallel systems. We also demonstrate the importance of the transient miss ratio, which is introduced in this paper and analyzed for the first time."

Analysis of the Impact of Memory in Distributed Parallel Processing Systems

Vinod G. J. Peris

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