On rotations in fringe-balanced binary trees

Information Processing Letters

Volumn 65, Issue 1, 1998, Pages 41-46

  Mahmoud, Hosam M ^a  

^a GEORGE WASHINGTON UNIVERSITY   (United States)

Author keywords

Data structures; Fringe balancing; Rotation; Tree

Indexed keywords

EID: 0002932874     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0020-0190(97)00184-1     Document Type: Article

References (27)

1. G. Adel'son-Vel'skii, E. Landis, An algorithm for the organization of information, Dokl. Akad. Nauk SSSR 146 (1962) 263-266; English translation in: Soviet. Math. Dokl. 3 (1962) 1259-1263.
2. G. Adel'son-Vel'skii, E. Landis, An algorithm for the organization of information, Dokl. Akad. Nauk SSSR 146 (1962) 263-266; English translation in: Soviet. Math. Dokl. 3 (1962) 1259-1263.
3. D. Aldous, B. Flannery, J. Palacios, Two applications of urn processes; the fringe analysis of search trees and the simulation of quasi-stationary distributions of Markov chains, Probab. Engineering Inform. Sci. 2 (1988) 293-307.
4. K. Athreya, S. Karlin, Embedding of urn schemes into continuous time Markov branching process and related limit theorem, Ann. Math. Statist. 39 (1968) 1801-1817.
5. K. Athreya, P. Ney, Branching Processes, Springer, New York, 1972.
6. A. Bagchi, A. Pal, Asymptotic normality in the generalized Pólya-Eggenbergerurn model, with applications to computer data structures, SIAM J. Algebraic Discrete Methods 6 (1985) 394-405.
7. W. Cunto, J. Gascón, Improving time and space efficiency in generalized binary search trees, Acta Inform. 24 (1987) 583-594.
8. L. Devroye, Limit laws for local counters in random binary search trees, Random Structures and Algorithms 2 (1991) 303-315.
9. B. Eisenbarth, N. Ziviani, G. Gonnet, K. Mehlhom, D. Wood, The theory of fringe analysis and its application to 2-3 trees and B-trees, Inform. and Control 55 (1982) 125-175.
10. J. Gastwirth, P. Bhattacharya, Two probability models of pyramids or chain letter schemes demonstrating that their promotional claims are unreliable, Oper. Res. 32 (1984) 527-536.
11. R. Gouet, A martingale approach to strong convergence in a generalized Pólya-Eggenberger urn model, Statist. Probab. Lett. 8 (1989) 225-228.
12. R. Gouet, Martingale functional central limit theorems for a generalized Pólya urn, Ann. Probab. 21 (1993) 1624-1639.
13. D. Knuth, The Art of Computer Programming, Vol. 3: Sorting and Searching, Addison-Wesley, Reading, MA, 1973.
14. H. Mahmoud, Evolution of Random Search Trees, Wiley, New York, 1992.
15. H. Mahmoud, R. Smythe, On the distribution of leaves in rooted subtrees of recursive trees, Ann. Appl. Probab. 1 (1991) 406-418.
16. H. Mahmoud, R. Smythe, Asymptotic joint normality of outdegrees of nodes in random recursive trees. Random Structures and Algorithms 3 (1992) 255-266.
17. H. Mahmoud, R. Smythe, Probabilistic Analysis of bucket recursive trees, Theoret. Comput. Sci. 144 (1995) 221-249.
18. H. Mahmoud, R. Smyhte, J. Szymariski, On the structure of random plane-oriented recursive trees and their branches, Random Structures and Algorithms 4 (1993) 151-176.
19. J. Nievergelt, E. Reingold, Binary search trees of bounded balance, SIAM J. Comput. 2 (1973) 33-43.
20. P. Poblete, J. Munro, The analysis of a fringe heuristic for binary search trees, J. Algorithms 6 (1985) 336-350.
21. R. Sedgewick, P. Flajolet, Analysis of Algorithms, Addison-Wesley, Reading, MA, 1996.
22. R. Smythe, Central limit theorems for urn models, Stochastic Processes Appl. 65 (1996) 115-137.
23. W. Walker, D. Wood, Locally balanced binary search trees, Comput. J. 19 (1976) 322-325.
24. A. Yao, On random 2-3 trees, Acta Inform. 9 (1978) 159-170.
25. R. Yates, Some average measures in m-ary search trees, Inform. Process. Lett. 25 (1987) 375-381.
26. +-trees with partial expansions, IEEE Trans. Knowledge and Data Engineering 1 (1989) 248-257.
27. R. Yates, P. Poblete, Higher order analysis of 2-3 trees, Internat. J. Foundations Comput. Sci. 6 (1995) 1-10.