article

Open access

A fast algorithm for finding dominators in a flowgraph

Editor: Susan L. Graham Authors:

Thomas Lengauer,

Robert Endre TarjanAuthors Info & Claims

ACM Transactions on Programming Languages and Systems (TOPLAS), Volume 1, Issue 1

Pages 121 - 141

https://doi.org/10.1145/357062.357071

Published: 01 January 1979 Publication History

PDF eReader

Abstract

A fast algorithm for finding dominators in a flowgraph is presented. The algorithm uses depth-first search and an efficient method of computing functions defined on paths in trees. A simple implementation of the algorithm runs in O(m log n) time, where m is the number of edges and n is the number of vertices in the problem graph. A more sophisticated implementation runs in O(mα(m, n)) time, where α(m, n) is a functional inverse of Ackermann's function.

Both versions of the algorithm were implemented in Algol W, a Stanford University version of Algol, and tested on an IBM 370/168. The programs were compared with an implementation by Purdom and Moore of a straightforward O(mn)-time algorithm, and with a bit vector algorithm described by Aho and Ullman. The fast algorithm beat the straightforward algorithm and the bit vector algorithm on all but the smallest graphs tested.

References

[1]

ACKERMA~N, W. Zum Hilbertschen Aufbau der reellen Zahlen. Math. Ann. 99 (1928), 118-133.

Google Scholar

[2]

AMo, A.V., A~D ULLMA~q, J.D. The Theory of Parsing, Translation, and Compiling, Vol. II: Compiling. Prentice-Hall, Englewood Cliffs, N.J., 1972.

Crossref

Google Scholar

[3]

Axo, A.V., AND ULLMAS, J.D. Principles of Compiler Design. Addison-Wesley, Reading, Mass., 1977.

Google Scholar

[4]

HEcuT, M.S., ANo ULLMAS, J.D. A simple algorithm for global data flow analysis problems. SIAM J. Comput. 4 (I973), 519-532.

Google Scholar

[5]

K~uTH, D.E. The Art of Computer Programming, Vol. 1: Fundamental Algorithms. Addison- Wesley, Reading, Mass., 1968.

Crossref

Google Scholar

[6]

LORRY, E.S., ASr) MSOLOCK, C.W. Object code optimization. Comm. ACM/2, I (Jan. 1969), 13- 22.

Crossref

Google Scholar

[7]

PURDOM, P.W., AND MOORE, E.F. Algorithm 430: Immediate predominators in a directed graph. Comm. ACM 15, 8 (Aug. 1972), 777-778.

Crossref

Google Scholar

[8]

REIF, J. Combinatorial aspects of symbolic program analysis. Tech. Rep. TR-11-77, Center for Research in Computing Technology, Harvard U., Cambridge, Mass., 1977.

Google Scholar

[9]

TARJA~, R.E. Depth-first search and linear graph algorithms. SIAM J. Comptng. I (1972), 146- 160.

Google Scholar

[10]

TARJA~, R. Finding dominators in directed graphs SIAM J. Comptng. 3 (1974), 62-89.

Google Scholar

[11]

TARJAN, R.E. Edge-disjoint spanning trees, dominators, and depth-first search. Tech. Rep. STAN-CS-74-455, Comptr. Sci. Dept., Stanford U., Stanford, Calif., 1974.

Crossref

Google Scholar

[12]

TARJAN, R.E. Applications of path compression on balanced trees. Tech. Rep. STAN-CS-75-512, Comptr. Sci. Dept., Stanford U., Stanford, Calif., 1975.

Crossref

Google Scholar

[13]

TARJAN, R.E. Solving path problems on directed graphs. Tech. Rep. STAN-CS-528, Comptr. Sci. Dept., Stanford U., Stanford, Calif., 1975.

Crossref

Google Scholar

[14]

TARJAN, R.E. Applications of path compression on balanced trees. To appear in J. ACM.

Crossref

Google Scholar

Cited By

View all

Wang JWu YWang XZhang YQin LZhang WLin X(2024)Efficient Influence Minimization via Node BlockingProceedings of the VLDB Endowment10.14778/3675034.367504217:10(2501-2513)Online publication date: 1-Jun-2024
https://dl.acm.org/doi/10.14778/3675034.3675042
Maroun ESchoeberl MPuschner P(2024)Predictable and optimized single-path code for predicated processorsJournal of Systems Architecture10.1016/j.sysarc.2024.103214154(103214)Online publication date: Sep-2024
https://doi.org/10.1016/j.sysarc.2024.103214
Driessen SDi Nucci DTamburri Dvan den Heuvel W(2024)SolARScience of Computer Programming10.1016/j.scico.2023.103036232:COnline publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1016/j.scico.2023.103036
Show More Cited By

Index Terms

A fast algorithm for finding dominators in a flowgraph
1. Software and its engineering
  1. Software creation and management
    1. Software development techniques
      1. Flowcharts
  2. Software notations and tools
    1. General programming languages
      1. Language features

Recommendations

Finding dominators revisited: extended abstract
SODA '04: Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms

The problem of finding dominators in a flowgraph arises in many kinds of global code optimization and other settings. In 1979 Lengauer and Tarjan gave an almost-linear-time algorithm to find dominators. In 1985 Harel claimed a linear-time algorithm, but ...
A fast algorithm for finding common multiple-vertex dominators in circuit graphs
ASP-DAC '05: Proceedings of the 2005 Asia and South Pacific Design Automation Conference

In this paper we present a fast algorithm for computing common multiple-vertex dominators in circuit graphs. Dominators are widely used in CAD applications such as satisfiability checking, equivalence checking, ATPG, technology mapping, decomposition of ...
A new, simpler linear-time dominators algorithm

We present a new linear-time algorithm to find the immediate dominators of all vertices in a flowgraph. Our algorithm is simpler than previous linear-time algorithms: rather than employ complicated data structures, we combine the use of microtrees and ...

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Programming Languages and Systems

ACM Transactions on Programming Languages and Systems Volume 1, Issue 1

July 1979

153 pages

ISSN:0164-0925

EISSN:1558-4593

DOI:10.1145/357062

Editor:
Susan L. Graham

Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 January 1979

Published in TOPLAS Volume 1, Issue 1

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

506
Total Citations
View Citations
6,329
Total Downloads

Downloads (Last 12 months)691
Downloads (Last 6 weeks)46

Reflects downloads up to 03 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Wang JWu YWang XZhang YQin LZhang WLin X(2024)Efficient Influence Minimization via Node BlockingProceedings of the VLDB Endowment10.14778/3675034.367504217:10(2501-2513)Online publication date: 1-Jun-2024
https://dl.acm.org/doi/10.14778/3675034.3675042
Maroun ESchoeberl MPuschner P(2024)Predictable and optimized single-path code for predicated processorsJournal of Systems Architecture10.1016/j.sysarc.2024.103214154(103214)Online publication date: Sep-2024
https://doi.org/10.1016/j.sysarc.2024.103214
Driessen SDi Nucci DTamburri Dvan den Heuvel W(2024)SolARScience of Computer Programming10.1016/j.scico.2023.103036232:COnline publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1016/j.scico.2023.103036
Chen HDeng XWang YWu YZhao DAgmon NAn BRicci AYeoh W(2023)Sybil-Proof Diffusion Auction in Social NetworksProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3598787(1379-1387)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.5555/3545946.3598787
Baswana SBhanja KPandey A(2023)Minimum+1 (s, t)-cuts and Dual-edge Sensitivity OracleACM Transactions on Algorithms10.1145/362327119:4(1-41)Online publication date: 14-Oct-2023
https://dl.acm.org/doi/10.1145/3623271
Zhang PWu CPeng MZeng KYu DLai YKang YWang WWang ZDubach CBruening DHardekopf B(2023)Khaos: The Impact of Inter-procedural Code Obfuscation on Binary Diffing TechniquesProceedings of the 21st ACM/IEEE International Symposium on Code Generation and Optimization10.1145/3579990.3580007(55-67)Online publication date: 17-Feb-2023
https://dl.acm.org/doi/10.1145/3579990.3580007
Yan HZhang HShi JMa JXu X(2023)Toward Intelligent Fashion Design: A Texture and Shape Disentangled Generative Adversarial NetworkACM Transactions on Multimedia Computing, Communications, and Applications10.1145/356759619:3(1-23)Online publication date: 25-Feb-2023
https://dl.acm.org/doi/10.1145/3567596
Xu KLi WWang XHu XYan KWang XDong X(2023)CUR Transformer: A Convolutional Unbiased Regional Transformer for Image DenoisingACM Transactions on Multimedia Computing, Communications, and Applications10.1145/356612519:3(1-22)Online publication date: 25-Feb-2023
https://dl.acm.org/doi/10.1145/3566125
Constantinides ABelk MFidas CBeumers RVidal DHuang WBowles JWebber TSilvina APitsillides A(2023)Security and Usability of a Personalized User Authentication Paradigm: Insights from a Longitudinal Study with Three Healthcare OrganizationsACM Transactions on Computing for Healthcare10.1145/35646104:1(1-40)Online publication date: 27-Feb-2023
https://dl.acm.org/doi/10.1145/3564610
Akbari FSartipi KArcher N(2023)Synthetic Behavior Sequence Generation Using Generative Adversarial NetworksACM Transactions on Computing for Healthcare10.1145/35639504:1(1-23)Online publication date: 27-Feb-2023
https://dl.acm.org/doi/10.1145/3563950
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Abstract

References

Cited By

Index Terms

Recommendations

Finding dominators revisited: extended abstract

A fast algorithm for finding common multiple-vertex dominators in circuit graphs

A new, simpler linear-time dominators algorithm

Comments

Information

Published In

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations