General techniques for analyzing recursive algorithms with applications

SIAM Journal on Computing

Volumn 26, Issue 2, 1997, Pages 568-581

  Verma, Rakesh M ^a  

^a University of Houston   (United States)

Author keywords

Analysis of algorithms; Associative commutative (AC) matching; Divide and conquer; Graph algorithms; Problem complexity; Recurrences; Subtree isomorphism

Indexed keywords

EID: 4243168523     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539792240583     Document Type: Article

References (27)

1. A. AHO, J. HOPCROFT, AND J. ULLMAN, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974.
2. 1.5 √m/logn), Inform. Process. Lett., 37 (1991), pp. 237-240.
3. J. BENTLEY, D. HAKEN, AND J. SAXE, A general method for solving divide-and-conquer recurrences, SIGACT News, 12 (1980), pp. 36-44.
4. M. BLUM, R. FLOYD, V. PRATT, R. RIVEST, AND R. TARJAN, Time bounds for selection, J. Comput. System Sci., 7 (1972), pp. 448-461.
5. G. BRASSARD AND P. BRATLEY, Algorithmics: Theory and Practice, Prentice-Hall, Englewood Cliffs, NJ, 1988.
6. 2.5) time algorithms for the subgraph homeomorphism problem on trees, J. Algorithms, 8 (1987), pp. 106-112.
7. T. CORMEN, C. LEISERSON, AND R. RIVEST, Introduction to Algorithms, MIT Press/McGraw-Hill, Cambridge, MA, New York, 1990.
8. T. FEDER AND R. MOTWANI, Clique partitions, graph compression and speeding-up algorithms, in Proc. ACM Symposium on Theory of Computing, ACM, New York, 1991, pp. 123-133.
9. H. GABOW AND R. TARJAN, Almost-optimal speedups of algorithms for matching and related problems, in Proc. ACM Symposium on Theory of Computing, ACM, New York, 1988, pp. 514-527.
10. A. GOLDBERG, S. PLOTKIN, AND P. VAIDYA, Sublinear-time parallel algorithms for matching and related problems, in Proc. IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1988, pp. 174-185.
11. D. GREENE AND D. KNUTH, Mathematics for the Analysis of Algorithms, Birkhäuser, Boston, 1982.
12. G. HARDY, J. LITTLEWOOD, AND G. POLYA, Inequalities, Cambridge University Press, Cambridge, UK, 1952.
13. 5/2 algorithm for maximum matching in bipartite graphs, SIAM J. Comput., 2 (1973), pp. 225-231.
14. P. PURDOM JR. AND C. BROWN, The Analysis of Algorithms, Oxford University Press, Oxford, UK, 1985.
15. R. KARP, Probabilistic recurrence relations, in Proc. ACM Symposium on Theory of Computing, ACM, New York, 1991, pp. 190-197.
16. P. KILPELAINEN, Tree matching problems with applications to databases, Ph.D. thesis, University of Helsinki, Helsinki, 1992.
17. M. VAN KREVELD, M. OVERMARS, AND P. AGARWAL, Intersection queries in sets of disks, in Proc. Scandinavian Workshop on Algorithm Theory, Lecture Notes in Comput. Sci. 447, Springer-Verlag, Berlin, 1990, pp. 393-403; BIT, 32 (1992), pp. 268-279.
18. M. VAN KREVELD, M. OVERMARS, AND P. AGARWAL, Intersection queries in sets of disks, in Proc. Scandinavian Workshop on Algorithm Theory, Lecture Notes in Comput. Sci. 447, Springer-Verlag, Berlin, 1990, pp. 393-403; BIT, 32 (1992), pp. 268-279.
19. D. MITRINOVIC, Analytic Inequalities, Springer-Verlag, Berlin, 1970.
20. L. MONIER, Combinatorial solutions of multidimensional divide-and-conquer recurrences, J. Algorithms, 1 (1980), pp. 60-74.
21. S. W. REYNER, An analysis of a good algorithm for the subtree problem, SIAM J. Comput., 6 (1977), pp. 730-732.
22. R. M. VERMA, An error in Reyner's "An analysis of a good algorithm for the subtree problem," Technical Report 88/03, Computer Science Department, State University of New York at Stony Brook, Stony Brook, NY, 1988.
23. R. M. VERMA, A general method and a master theorem for divide-and-conquer recurrences with applications, J. Algorithms, 16 (1994), pp. 67-79.
24. R. M. VERMA AND I. V. RAMAKRISHNAN, Tight complexity bounds for term matching problems, Inform. and Comput., 101 (1992), pp. 33-69.
25. R. M. VERMA AND I. V. RAMAKRISHNAN, Some complexity theoretic aspects of AC Rewriting, in Proc. Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Comput. Sci. 349, Springer-Verlag, Berlin, 1989, pp. 407-420.
26. R. M. VERMA AND S. W. REYNER, An analysis of a good algorithm for the subtree problem, corrected, SIAM J. Comput., 18 (1989), pp. 906-908.
27. L. ZHIYUAN AND E. REINGOLD, Solution of a divide-and-conquer maximin recurrence, SIAM J. Comput., 18 (1989), pp. 1188-1200.