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Operations on sparse relations

Authors:

H. B. Hunt, III,

J. D. Ullman,

T. G. SzymanskiAuthors Info & Claims

Communications of the ACM, Volume 20, Issue 3

Pages 171 - 176

https://doi.org/10.1145/359436.359446

Published: 01 March 1977 Publication History

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Abstract

Various computations on relations, Boolean matrices, or directed graphs, such as the computation of precedence relations for a context-free grammar, can be done by a practical algorithm that is asymptotically faster than those in common use. For example, how to compute operator precedence or Wirth-Weber precedence relations in O(n²) steps is shown, as well as how to compute linear precedence functions in O(n) steps, where n is the size of a grammar. The heart of the algorithms is a general theorem giving sufficient conditions under which an expression whose operands are sparse relations and whose operators are composition, transitive closure, union, and inverse, can be computed efficiently.

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Cited By

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Brüggemann-Klein AWood D(2003)On predictive parsing and extended context-free grammarsComputer Science in Perspective10.5555/865449.865456(69-87)Online publication date: 1-Jan-2003
https://dl.acm.org/doi/10.5555/865449.865456
Brüggemann-Klein AWood D(2003)On Predictive Parsing and Extended Context-Free GrammarsComputer Science in Perspective10.1007/3-540-36477-3_6(69-87)Online publication date: 28-Feb-2003
https://doi.org/10.1007/3-540-36477-3_6
Yannakakis M(1996)Perspectives on database theoryACM SIGACT News10.1145/235666.23567027:3(25-49)Online publication date: 1-Sep-1996
https://dl.acm.org/doi/10.1145/235666.235670
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Index Terms

Operations on sparse relations
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory

Index terms have been assigned to the content through auto-classification.

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Published In

Communications of the ACM Volume 20, Issue 3

March 1977

80 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/359436

Editor:
Robert L. Ashenhurst
Univ. of Chicago, Chicago, IL

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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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Publication History

Published: 01 March 1977

Published in CACM Volume 20, Issue 3

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Brüggemann-Klein AWood D(2003)On predictive parsing and extended context-free grammarsComputer Science in Perspective10.5555/865449.865456(69-87)Online publication date: 1-Jan-2003
https://dl.acm.org/doi/10.5555/865449.865456
Brüggemann-Klein AWood D(2003)On Predictive Parsing and Extended Context-Free GrammarsComputer Science in Perspective10.1007/3-540-36477-3_6(69-87)Online publication date: 28-Feb-2003
https://doi.org/10.1007/3-540-36477-3_6
Yannakakis M(1996)Perspectives on database theoryACM SIGACT News10.1145/235666.23567027:3(25-49)Online publication date: 1-Sep-1996
https://dl.acm.org/doi/10.1145/235666.235670
Yannakakis M(1995)Perspectives on database theoryProceedings of IEEE 36th Annual Foundations of Computer Science10.1109/SFCS.1995.492479(224-246)Online publication date: 1995
https://doi.org/10.1109/SFCS.1995.492479
Grahne GSippu SSoisalon-Soininen E(1991)Efficient evaluation for a subset of recursive queriesJournal of Logic Programming10.1016/0743-1066(91)90039-R10:3-4(301-332)Online publication date: 1-Mar-1991
https://dl.acm.org/doi/10.1016/0743-1066%2891%2990039-R
Yannakakis MRosenkrantz DSagiv Y(1990)Graph-theoretic methods in database theoryProceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems10.1145/298514.298576(230-242)Online publication date: 2-Apr-1990
https://dl.acm.org/doi/10.1145/298514.298576
Grahne GSippu SSoisalon-Soininen E(1987)Efficient evaluation for a subset of recursive queriesProceedings of the sixth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems10.1145/28659.28690(284-293)Online publication date: 1-Jun-1987
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Gough K(1985)A new method of generating LL(1) lookahead setsACM SIGPLAN Notices10.1145/988336.98833820:6(16-19)Online publication date: 1-Jun-1985
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Sippu SSoisalon-Soininen E(1985)On the use of relational expressions in the design of efficient algorithmsAutomata, Languages and Programming10.1007/BFb0015771(456-464)Online publication date: 1985
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Sippu SSoisalon-Soininen E(1983)On the complexity of LL(k) testingJournal of Computer and System Sciences10.1016/0022-0000(83)90015-626:2(244-268)Online publication date: Apr-1983
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Abstract

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A modification of Warshall's algorithm for the transitive closure of binary relations

Evaluating Relational Expressions with Dense and Sparse Arguments

Modified Rate-Monotonic Algorithm for Scheduling Periodic Jobs with Deferred Deadlines

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