Abstract
Recently it has been discovered that control flow graphs of structured programs have bounded treewidth. In this paper we show that this knowledge can be used to design fast algorithms for control flow analysis. We give a linear time algorithm for the problem of finding the immediate multiple-vertex dominator set for all nodes in a control flow graph. The problem was originally proposed by Gupta (Generalized dominators and post-dominators, ACM Symp. on Principles of Programming Languages, 1992). Without the restriction of bounded treewidth the fastest algorithm runs in O(¦V¦*¦E¦) on a graph with ¦V¦ nodes and ¦E¦ edges and is due to Alstrup, Clausen and JØrgensen (An O(¦V¦*¦E¦) Algorithm for Finding Immediate Multiple-Vertex Dominators, accepted to Information Processing Letters).
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A.V. Aho, R. Sethi, and J.D. Ullman. Compilers: Principles, Techniques and Tools. Addison-Wesley, 1986.
S. Alstrup, J. Clausen, and K. JØrgensen. An O(¦V¦*¦E¦) algorithm for finding immediate multiple-vertex dominators. Technical Report DIKU-TR-96/4, Deparment of Computer Science, University of Copenhagen, 1996. Revised version with minor change accepted to Information Processing Letters.
H. Bodlaender. A linear time algorithm for finding tree-decompositions of small treewidth. In Proc. 25th ACM. Symp. on theory of Comp.(STOC'93), pages 226–234, 1993.
G.R. Gao, Y.-F Lee, and V.C. Sreedhar. DJ-graphs and their application to flow-graph analyses. Technical Report 70, McGill University, School of Computer Science, ACAPS, May 1994.
G.R. Gao and V.C. Sreedhar. A linear time algorithm for placing Φ-nodes. In ACM Symp. on the Principles of Programming Languages (POPL'95), volume 22, pages 62–73, January 1995.
R. Gupta. Generalized dominators and post-dommators. In ACM Symp. on Principles of Programming Languages (POPL'92), volume 19, pages 246–257, 1992.
R. Gupta. Generalized dominators. Information processing letters, 53:193–200, 1995.
D. Harel. A linear time algorithm for finding dominator in flow graphs and related problems. In Proc. 17th Ann. ACM Symp. on theory of Comp. (STOC'85), pages 185–194, 1985.
M.S. Hecht and J.D. Ullman. A simple algorithm for global data flow analysis of programs. SIAM J. Comput., 4:519–532, 1975.
B.R. Kernighan and D.M. Ritchie. The C programming language. Prentice-Hall, New-Jersey, 1978.
T. Lengauer and R.E. Tarjan. A fast algorithm for finding dominators in a flow-graph. ACM Trans. Programming Languages Systems, 1:121–141, 1979.
P. Naur. Revised report on the algorithmic language algol 60. Comm. ACM, 1(6):1–17, 1963.
P.W. Purdom and E.F. Moore. Immediate predominators in a directed graph. Comm. ACM, 15(8):777–778, 1972.
R.E. Tarjan. Finding dominators in directed graphs. SIAM J. Comput., 3(1):62–89, 1974.
M. Thorup. Structured programs have small tree-width and good register allocation. Technical Report DIKU-TR-95/18 (revised version), Deparaient of Computer Science, University of Copenhage, 1995.
N. Wirth. The programming language pascal. Acta informatica, 1:35–63, 1971.
N. Wirth. Programming in modula-2(3rd corr.ed). Springer-verlag, Berlin, New York, 1985.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Alstrup, S., Lauridsen, P.W., Thorup, M. (1996). Generalized dominators for structured programs. In: Cousot, R., Schmidt, D.A. (eds) Static Analysis. SAS 1996. Lecture Notes in Computer Science, vol 1145. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61739-6_32
Download citation
DOI: https://doi.org/10.1007/3-540-61739-6_32
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61739-6
Online ISBN: 978-3-540-70674-8
eBook Packages: Springer Book Archive