NDLI: Multiphase complete exchange: a theoretical analysis

Content Provider	IEEE Xplore Digital Library
Author	Bokhari, S.H.
Copyright Year	1968
Abstract	Complete exchange requires each of N processors to send a unique message to each of the remaining N-1 processors. For a circuit switched hypercube with N=2/sup d/ processors, the direct and standard algorithms for complete exchange are time optimal for very large and very small message sizes, respectively. For intermediate sizes, a hybrid multiphase algorithm is better. This carries out direct exchanges on a set of subcubes whose dimensions are a partition of the integer d. The best such algorithm for a given message size m could hitherto only be found by enumerating all partitions of d. The multiphase algorithm is analyzed assuming a high performance communication network. It is proved that only algorithms corresponding to equipartitions of d (partitions in which the maximum and minimum elements differ by at most one) can possibly be optimal. The runtimes of these algorithms plotted against m form a hull of optimality. It is proved that, although there is an exponential number of partitions: (1) the number of faces on this hull is /spl Theta/(/spl radic/(d)); (2) the hull can be found in /spl Theta/(/spl radic/(d)) time; and (3) once it has been found, the optimal algorithm for any given m can be found in /spl Theta/(log d) time. These results provide a very fast technique for minimizing communication overhead in many important applications, such as matrix transpose, fast Fourier transform, and alternating directions implicit (ADI).
Sponsorship	IEEE Computer Society Technical Committee on Distributed Process IEEE Computer Society Technical Committee on VLSI IEEE Technical Committee on Computer Architecture IEEE Computer Society
Starting Page	220
Ending Page	229
Page Count	10
File Size	1052041
File Format	PDF
ISSN	00189340
Volume Number	45
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1996-02-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Partitioning algorithms Hypercubes Algorithm design and analysis Circuits Scheduling algorithm Concurrent computing Distributed computing Partial differential equations Multiprocessor interconnection networks Power measurement
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Software Hardware and Architecture

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