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The complexity of parallel evaluation of linear recurrence

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L. Hyafil,

H. T. KungAuthors Info & Claims

STOC '75: Proceedings of the seventh annual ACM symposium on Theory of computing

Pages 12 - 22

https://doi.org/10.1145/800116.803748

Published: 05 May 1975 Publication History

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Abstract

The concept of computers such as C.mmp and ILLIAC IV is to achieve computational speed-up by performing several operations simultaneously with parallel processors. This type of computer organization is referred to as a parallel computer. In this paper, we prove upper bounds on speed-ups achievable by parallel computers for a particular problem, the solution of first order linear recurrences. We consider this problem because it is important in practice and also because it is simply stated so that we might obtain some insight into the nature of parallel computation by studying it.

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Hyafil, L. and H. T. Kung {75}. Bounds on the speed-ups of Parallel Evaluation of Recurrences, Computer Science Department Report, Carnegie-Mellon University.

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Valiant L(2005)Graph-theoretic arguments in low-level complexityMathematical Foundations of Computer Science 197710.1007/3-540-08353-7_135(162-176)Online publication date: 24-May-2005
https://doi.org/10.1007/3-540-08353-7_135
Mikloško JKotov V(1984)Complexity of Parallel AlgorithmsAlgorithms, Software and Hardware of Parallel Computers10.1007/978-3-662-11106-2_2(45-63)Online publication date: 1984
https://doi.org/10.1007/978-3-662-11106-2_2
Cohen JHickey TKatcoff J(1982)Upper Bounds for Speedup in Parallel ParsingJournal of the ACM (JACM)10.1145/322307.32231629:2(408-428)Online publication date: Apr-1982
https://doi.org/10.1145/322307.322316
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The complexity of parallel evaluation of linear recurrence

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STOC '75: Proceedings of the seventh annual ACM symposium on Theory of computing

May 1975

265 pages

ISBN:9781450374194

DOI:10.1145/800116

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Published: 05 May 1975

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STOC '75 Paper Acceptance Rate 31 of 87 submissions, 36%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Valiant L(2005)Graph-theoretic arguments in low-level complexityMathematical Foundations of Computer Science 197710.1007/3-540-08353-7_135(162-176)Online publication date: 24-May-2005
https://doi.org/10.1007/3-540-08353-7_135
Mikloško JKotov V(1984)Complexity of Parallel AlgorithmsAlgorithms, Software and Hardware of Parallel Computers10.1007/978-3-662-11106-2_2(45-63)Online publication date: 1984
https://doi.org/10.1007/978-3-662-11106-2_2
Cohen JHickey TKatcoff J(1982)Upper Bounds for Speedup in Parallel ParsingJournal of the ACM (JACM)10.1145/322307.32231629:2(408-428)Online publication date: Apr-1982
https://doi.org/10.1145/322307.322316
Cei SGalli MSoccio MZellini P(1981)On some parallel algorithms for inverting tridiagonal and pentadiagonal matricesCalcolo10.1007/BF0257643318:4(303-319)Online publication date: Dec-1981
https://doi.org/10.1007/BF02576433
Heller D(1979)Minimal parallelism for associative computations under time constraintsMinimaler Parallelismus für zeitbeschränkte assoziative BerechnungenComputing10.1007/BF0225312322:2(101-118)Online publication date: Jun-1979
https://doi.org/10.1007/BF02253123
Weide B(1977)A Survey of Analysis Techniques for Discrete AlgorithmsACM Computing Surveys (CSUR)10.1145/356707.3567119:4(291-313)Online publication date: Dec-1977
https://doi.org/10.1145/356707.356711

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An Algorithm for Solving Linear Recurrence Systems on Parallel and Pipelined Machines

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An Algorithm for Solving Linear Recurrence Systems on Parallel and Pipelined Machines

Time and Parallel Processor Bounds for Linear Recurrence Systems

Parallel Recurrence Solvers for Vector and SIMD Supercomputers

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