Acta Informatica

, Volume 24, Issue 5, pp 583–594 | Cite as

Improving time and space efficiency in generalized binary search trees

  • Walter Cunto
  • Jose Luis Gascon


This paper deals with main memory data structures for which time and space performance are simultaneously considered. The main contribution is a new data structure called Generalised Binary Search Tree (GBS-tree) together with searching and updating algorithms on this structure. GBS-trees generalise different data structures based on binary trees that have appeared in the literature. A k-t GBS-tree allows up to t keys per node and subtrees in the tree's fringe of exactly 2k-1 full nodes are kept balanced. Their time and space performances are analysed in depth. The time performance is expressed in terms of the average and the variance of the number of binary comparisons between a given key and keys already in the structure. The space performance measures both the space used to space generated ratio (space utilization factor) and the pointers to keys ratio of these trees. The analysis shows that the time performance always improves when GBS-trees of higher order are considered. In the absence of balancing techniques, larger values of t, which produces smaller pointers to key ratios, induce unacceptably poor space utilizations factors. We show that both pointers to keys ratio and space utilization factor improve when larger values of k are used. Thus, local balancing techniques are adequate, not only for time performance improvement, but also, for space performance improvement.


Time Performance Space Performance Binary Tree Search Tree Main Memory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Adel'son-Vel'skii, G.M., Landins, E.M.: An Algorithm for the Organization of Information. Doklady Akademia Nauk USSR 146, 263–266 (1962)MathSciNetGoogle Scholar
  2. 2.
    Bell, C.J.: An Investigation into the Principles of the Classification and Analysis on an Automatic Digital Computer. Doctoral Thesis, Leeds University 1965Google Scholar
  3. 3.
    Bentley, J.L.: Multidimensional Binary Search Trees Use for Associative Searching. Commun ACM 18, 509–517 (1975)CrossRefGoogle Scholar
  4. 4.
    Cunto, W., Lau, G.: Generalised Multidimensional Trees. TECH-REP CSC 87-02 Centro Cientifico IBM de VenezuelaGoogle Scholar
  5. 5.
    Eisenbarth, B., Ziviani, N., Gonnet, G.H., Melhorn, K., Wood, D.: The Theory of Fringe Analysis and its Application to 2–3 Trees and B-trees. Inf. Control 55, 125–174 (1984)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Gonnet, G.H.: Balancing Binary Trees by Internal Path Reduction. Commun. ACM 26, 1074–1081 (1983)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Gonnet, G.H.: Handbook of Algorithms and Data Structures. Reading, MA.: Addison Wesley 1984zbMATHGoogle Scholar
  8. 8.
    Knuth, D.E.: The Art of Computer Programming, Vol. I. Fundamental Algorithms. 2nd Ed. Reading, MA.: Addison Wesley 1973Google Scholar
  9. 9.
    Knuth, D.E.: The Art of Computer Programming, Vol. III. Sorting and Searching, Reading, MA.: Addison Wesley 1973zbMATHGoogle Scholar
  10. 10.
    Kuspert, K.: Storage Utilization in B-trees with a Generalized Overflow Technique. Acta Inf. 19, 33–55 (1983)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Nievergelt, J.: Binary Search Trees of Bounded Balance. SIAM J. Comput. 2, 33–43 (1973)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Poblete, P.V.: Fringe Tecniques for Binary Search Trees. Ph. D. Thesis, C.S. Dept., University of Waterloo 1982Google Scholar
  13. 13.
    Poblete, P.V., Munro J.I.: The Analysis of a Fringe Heuristic for Binary Search Trees. J. Algorithms 6, 336–350 (1985)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Walker, A., Wood, D.: Locally Balanced Binary Trees. Comput. J. 19, 322–325 (1976)CrossRefGoogle Scholar
  15. 15.
    Yao, A.: On Random 2–3 Trees. Acta Inf. 9, 159–170 (1978)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Walter Cunto
    • 1
  • Jose Luis Gascon
    • 2
  1. 1.Centro Cientifico IBM de VenezuelaCaracasVenezuela
  2. 2.Burroughs de VenezuelaCaracasVenezuela

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