Applications of Path Compression on Balanced Trees

Journal of the ACM (JACM)

Volumn 26, Issue 4, 1979, Pages 690-715

  Tarjan, Robert Endre ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

balanced tree; dominators; equivalence relation; global flow analysis; graph algorithm; minimum spanning tree; path compression; path problem; tree

Indexed keywords

COMPUTER PROGRAMMING - SUBROUTINES; MATHEMATICAL TECHNIQUES - TREES;

DATA PROCESSING;

EID: 0018533367     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/322154.322161     Document Type: Article

References (31)

1. Ackermann, W Zum Hilbershen Aufbau der reellen Zahlen. Math. Ann 99 (1928), 118-133.
2. Aho, A.V., Hopcroft, J.E., And Ullman, J.D. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Mass., 1974.
3. Aho, A.V., Hopcroft, J.E., And Ullman, J.D. On computing least common ancestors in trees SIAM J. Comptng. 5(1976), 115-132.
4. Aho, A V., And Ullman, J D. Node listings for reducible flow graphs. J Comptr Syst Sci. 13 (1976), 286-299.
5. Arden, B.W., Galler, B A., And Graham, R.M. An algorithm for equivalence declarations. Comm. ACM 4, 7 (July 1961), 310-314.
6. Cheriton, D, AND Tarjan, R E Finding minimum spanning trees SIAM J Comptng.5 (1976), 724-742.
7. Chin, F Y, And Houck, D J Algorithms for updating minimal spanning trees. J. Compir Syst Sci 16 (1978), 333-344.
8. Chvátal, V., Klarner, D.A., And Knuth, D E Selected combinatorial research problems STAN-CS-72-292, Comptr Sci Dept, Stanford U, Stanford, Calif, 1972.
9. Farrow, R Efficient on-line evaluation of functions defined on paths in trees. Tech. Rep. 476-093-17, Dept Math Sci, Rice U, Houston, Tex, 1977.
10. Fischer, M J. Efficiency of equivalence algorithms. In Complexity of Computations, R E Miller and J W Thatcher, Eds, Plenum Press, New York, 1972, pp 153-168.
11. Fono, A., Kam, J, AND Ullman, J D Application of lattice algebra to loop optimization. Conf. Rec Second ACM Symp. Principles of Programming Languages, Palo Alto, Calif., 1975, pp 1-9.
12. Galler, B A., And Fischer, M J An improved equivalence algorithm Comm. ACM 7, 5 (May 1964), 301-303.
13. Graham, S L, AND Wegman, M A fast and usually linear algorithm for global flow analysis. J. ACM 23, (Jan 1976), 172-202.
14. Hopcroft, J E Private communication.
15. Hopcroft, J E., And Ullman, J D Set merging algorithms. SIAM J Comping 2(1973), 294-303.
16. Hu, T C Integer Programming and Network Flows. Addison-Wesley, Reading, Mass., 1969, pp 129-150.
17. Kennedy, K.W. Node listings applied to data flow analysis Conf Rec. Second ACM Symp Principles of Programming Languages, Palo Alto, Calif, 1975, pp 10-21.
18. Knuth, D E The Art of Computer Programming, Vol I. Fundamental Algorithms, Addison-Wesley, Reading, Mass., 1968.
19. Lengauer, T., And Tarjan, R E A fast algorithm for finding dominators in a flow graph. To appear in ACM Trans Programming Languages and Sysl.
20. Paterson, M Unpublished report, U. of Warwick, Conventry, England, 1972.
21. Tarjan, R.E. Depth-first search and linear graph algorithms SIAM J. Comptng. 1(1972), 146-160.
22. Tarjan, R.E. Finding dominators m directed graphs. SIAM J. Comptng 5(1974), 62-89.
23. Tarjan, R.E. Testing flow graph reducibihty J Comptr and Syst. Sci 9 (1974), 355-365.
24. Tarjan, R E Efficiency of a good but not linear set union algorithm J. ACM 22, 2 (April 1975), 215-225.
25. Tarjan, R E. Applications of path compression on balanced trees Tech Rep. STAN-CS-75-512, Comptr. Sci Dept, Stanford U, Stanford, Calif., 1975.
26. Tarjan, R.E. Solving path problems on directed graphs Tech Rep STAN-CS-75-528, Comptr. Sci. Dept, Stanford U, Stanford, Calif, 1975.
27. Tarjan, R.E. Graph theory and Gaussian elimination In Sparse Matrix Computations, J R. Bunch and D.J. Rose, Eds., Academic Press, New York, 1976, pp. 3-22.
28. Tarjan, R E A Class Of Algorithms Which Require Non-Linear Time To Maintain Disjoint Sets To Appear In J. Comptr and Syst. Sci.
29. Tarjan, R.E. Complexity of monotone networks for computing conjunctions Annals Discrete Math. 2 (1978), 121-133.
30. Ullman, J.D. A fast algorithm for the elimination of common subexpressions. Acta Informatica 2(1973), 191-213.
31. Yao, A.C. An 0(|E| log log |V|)algorithm for finding minimum spanning trees. Inform. Processing Letters 4 (1975), 21-23.