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Node listings for reducible flow graphs

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J. D. UllmanAuthors Info & Claims

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

Pages 177 - 185

https://doi.org/10.1145/800116.803767

Published: 05 May 1975 Publication History

Abstract

In [1], Kennedy conjectures that for every n node reducible flow graph, there is a sequence of nodes (with repetitions) of length O(nlogn) such that all acyclic paths are subsequences thereof. Such a sequence would, if it could be found easily, enable one to do various kinds of global data flow analyses quickly. We show that for all reducible flow graphs such a sequence does exist, even if the number of edges is much larger than n. If the number of edges is O(n), the node listing can be found in O(nlogn) time.

References

[1]

K. Kennedy, "Node listing techniques applied to data flow analysis," Proc. 2nd ACM Conference on Principles of Programming Languages, January 1975, 10-21.

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[2]

F.E. Allen, "Control flow analysis," SIGPLAN Notices5:7, (July, 1970), 1-19.

Digital Library

[3]

D. E. Knuth, "An empirical study of FORTRAN programs," Software: Practice and Experience1:2, (April, 1971), 105-134.

[4]

M.S. Hecht and J. D. Ullman, "Analysis of a simple algorithm for global data flow problems," Proc. ACM Symposium on Principles of Programming Languages, October, 1973. To appear, SIAM J. Computing.

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[5]

J. Cocke, "Global common subexpression elimination," SIGPLAN Notices5:7 (July, 1970), 20-24.

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[6]

A.V. Aho and J. D. Ullman, The Theory of Parsing, Translation and Compiling, Volume 2, Compiling, Prentice-Hall, Englewood Cliffs, N. J., 1973.

Digital Library

[7]

M. Schaefer, A Mathematical Theory of Global Flow Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1973.

[8]

K. Kennedy, "A global flow analysis algorithm," Int. J. Comp. Math.3 (December, 1971), 5-15.

[9]

G.A. Kildall, "A unified approach to global program optimization," Proc. ACM Symposium on Principles of Programming Languages, October, 1973.

Digital Library

[10]

J. Kam and J. D. Ullman, "Global optimization problems and iterative algorithms," TR 146, Computer Science Laboratory, Princeton University, January, 1974.

[11]

S. L. Graham and M. Wegman, "A fast and usually linear algorithm for global flow analysis," Proc. 2nd ACM Symposium on Principles of Programming Languages, January, 1975.

Digital Library

[12]

C. M. Geschke, Global Program Optimizations, Ph. D. Thesis, Carnegie-Mellon University, 1972.

Digital Library

[13]

M. Newey, "Notes on a problem involving permutations as subsequences," STAN-CS-73-340, Computer Science Department, Stanford University, Stanford, California.

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[14]

M. S. Hecht and J. D. Ullman, "Flow graph reducibility," SIAM J. Computing1:2 (June, 1972), 188-202.

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[15]

M. S. Hecht and J. D. Ullman, "Characterizations of reducible flow graphs," J. ACM21:3 (July, 1974), 367-375.

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[16]

J. D. Ullman, "Fast algorithms for the elimination of common subexpressions," Acta Informatica2 (December, 1973), 191-213.

Digital Library

[17]

P. M. Lewis II, R. E. Stearns, and J. Hartmanis, "Memory bounds for recognition of context-free and context-sensitive languages," IEEE Conference Record of 6th Annual ACM Symposium on Switching Circuit Theory and Logical Design, October, 1966, pp. 191-202.

[18]

R. E. Tarjan, "Testing flow graph reducibility," J. Computer and System Sciences9:3 (December, 1974), 355-365.

Digital Library

[19]

G. Markowsky, Unpublished memorandum, December, 1974.

[20]

R. E. Tarjan, private communication, December, 1974.

Cited By

Dayarathna MSuzumura T(2013)Automatic optimization of stream programs via source program operator graph transformationsDistributed and Parallel Databases10.1007/s10619-013-7130-x31:4(543-599)Online publication date: 1-Dec-2013
https://dl.acm.org/doi/10.1007/s10619-013-7130-x
Joshi SShyamasundar RAggarwal S(2012)A New Method of MHP Analysis for Languages with Dynamic BarriersProceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops & PhD Forum10.1109/IPDPSW.2012.70(519-528)Online publication date: 21-May-2012
https://dl.acm.org/doi/10.1109/IPDPSW.2012.70
Fosdick LOsterweil L(2011)Data Flow Analysis In Software ReliabilityEngineering of Software10.1007/978-3-642-19823-6_5(49-85)Online publication date: 2011
https://doi.org/10.1007/978-3-642-19823-6_5
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Index Terms

Node listings for reducible flow graphs

Recommendations

Characterizations of Reducible Flow Graphs

It is established that if G is a reducible flow graph, then edge (n, m) is backward (a back latch) if and only if either n = m or m dominates n in G. Thus, the backward edges of a reducible flow graph are unique.

Further characterizations of reducibility ...
Node listings for reducible flow graphs

K. Kennedy recently conjectured that for every n node reducible flow graph, there is a sequence of nodes (with repetitions) of length O(n log n) such that all acyclic paths are subsequences thereof. Such a sequence would, if it could be found easily, ...
Feedback vertex sets and cyclically reducible graphs

The problem of finding a minimum cardinality feedback vertex set of a directed graph is considered. Of the classic NP-complete problems, this is one of the least understood. Although Karp showed the general problem to be NP-complete, a linear algorithm ...

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cover image ACM Conferences

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

May 1975

265 pages

ISBN:9781450374194

DOI:10.1145/800116

Copyright © 1975 ACM.

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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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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Cited By

Dayarathna MSuzumura T(2013)Automatic optimization of stream programs via source program operator graph transformationsDistributed and Parallel Databases10.1007/s10619-013-7130-x31:4(543-599)Online publication date: 1-Dec-2013
Joshi SShyamasundar RAggarwal S(2012)A New Method of MHP Analysis for Languages with Dynamic BarriersProceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops & PhD Forum10.1109/IPDPSW.2012.70(519-528)Online publication date: 21-May-2012
Fosdick LOsterweil L(2011)Data Flow Analysis In Software ReliabilityEngineering of Software10.1007/978-3-642-19823-6_5(49-85)Online publication date: 2011
Tok TGuyer SLin C(2006)Efficient flow-sensitive interprocedural data-flow analysis in the presence of pointersProceedings of the 15th international conference on Compiler Construction10.1007/11688839_3(17-31)Online publication date: 30-Mar-2006
Knoop JRüthing OSteffen B(2004)Lazy code motionACM SIGPLAN Notices10.1145/989393.98943939:4(460-472)Online publication date: 1-Apr-2004
Rüthing O(1998)Interacting code motion transformationsundefinedOnline publication date: 1-Jan-1998
Knoop J(1998)Optimal interprocedural program optimizationundefinedOnline publication date: 1-Jan-1998
Knoop JRüthing OSteffen B(1992)Lazy code motionACM SIGPLAN Notices10.1145/143103.14313627:7(224-234)Online publication date: 1-Jul-1992
Knoop JRüthing OSteffen BFeldman S(1992)Lazy code motionProceedings of the ACM SIGPLAN 1992 conference on Programming language design and implementation10.1145/143095.143136(224-234)Online publication date: 1-Jul-1992
Ramanathan JKennedy K(1981)Pathlistings applied to data flow analysisActa Informatica10.1007/BF0028930616:3(253-273)Online publication date: 1-Nov-1981
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