Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T03:56:45.792Z Has data issue: false hasContentIssue false
  • English
  • Français

Toward a Formal Derivation of the Expected Behavior of Prefix B-Trees

Published online by Cambridge University Press:  27 July 2009

Hosam M. Mahmoud  and
Ratko Orlandić
Hosam M. Mahmoud
Affiliation:
Department of Statistics, The George Washington University, Washington, D.C. 20052
Ratko Orlandić
Affiliation:
Department of Statistics, The George Washington University, Washington, D.C. 20052
Get access Rights & Permissions [Opens in a new window]

Abstract

Via order statistics we analyze the average length of all separators in random Prefix B-trees. From this result we draw some conclusions and conjectures concerning the average overall storage of random Prefix B-trees.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 2 , April 1995 , pp. 183 - 192
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Baeza-Yates, R.A. (1989). Expected behavior of B+-trees under random insertions. Acta Informatica 26: 439–471.Google Scholar
2.Bayer, R. & McCreight, E. (1972). Organization and maintenance of large ordered indexes. Acta Informatica 1: 173–189.Google Scholar
3.Bayer, R. & Unterauer, K. (1977). Prefix B-trees. ACM Transactions on Database Systems 2: 11–26.Google Scholar
4.Comer, D. (1979). The ubiquitous B-tree. Computing Surveys 11: 121–137.Google Scholar
5.Fagin, R., Nievergelt, J., Pippenger, N., & Strong, H.R. (1979). Extendible hashing: A fast access method for dynamic files. ACM Transactions on Database Systems 4: 315–344.Google Scholar
6.Ferguson, D.E. (1992). A data structure for fast file processing. Communications of the ACM 35: 114–120.CrossRefGoogle Scholar
7.Flajolet, P. & Richmond, B. (1992). Generalized digital trees and their difference-differential equations. Random Structures and Algorithms 3: 305–320.Google Scholar
8.Hoshi, M. & Flajolet, P. (1992). Page usage in quadtree indexes. BIT 32: 384–402.CrossRefGoogle Scholar
9.Knuth, D.E. (1973). The art of computer programming: Sorting and searching. Vol. 3. Reading, MA: Addison-Wesley.Google Scholar
10.Lew, W. & Mahmoud, H.M. (1994). The jointd distribution of elastic buckets in multiway search trees. SIAM Journal on Computing 23: 1050–1074.CrossRefGoogle Scholar
11.Litwin, W. (1980). Linear virtual hashing: A new tool for files and tables implementation. Proceedings of the 6th International Conference on Very Large Data Bases. Montreal, Que.: VLDB Endowment, pp. 212–223.Google Scholar
12.Mahmoud, H.M. (1992). Evolution of random search trees. New York: Wiley.Google Scholar
13.Mahmoud, H.M. & Papadakis, T. (1992). A probabilistic analysis of fixed and elastic buckets in tries and PATRICIA trees. Proceedings of the 30th Annual Allerton Conference on Communication, Control, and Computing. Monticello, IL: University of Illinois at Urbana-Champaign, pp. 874–883.Google Scholar
14.Orlandić, R. & Pfaltz, J.L. (1988). Compact O-complete trees. Proceedings of the 14th International Conference on Very Large Data Bases. Long Beach, CA: VLDB Endowment, pp. 372–381.Google Scholar
15.Orlandić, R. & Pfaltz, J.L. (1989). Analysis of compact O-complete trees: A new access method to large databases. Proceedings of the 7th FCT Conference, Szeged, Hungary. Published in Lecture Notes in Computer Science 380: 362–371.Google Scholar
16.Ross, S. (1988). A first course in probability, 3rd ed.New York: Macmillan.Google Scholar
17.Yao, A.C. (1978). On random 2–3 trees. Acta Informatica 9: 159–170.CrossRefGoogle Scholar