Abstract
This paper presents an analysis, a survey, and compares the pertinent characteristics of AVL and 2-3 trees. In an attempt to optimize the space complexity of 2-3 trees, it introduces a new space saving and efficient top-down insertion and construction algorithm. The analysis shows that neither data structure totally dominates the other. The decision as to which is cost-wise efficient is a function of the application.
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References
A. V. Aho, J. E. Hopcroft, and J. D. Ullman,The Design and Analysis of Computer Algorithms (Addison-Wesley, Reading, Mass., 1975).
J. L. Baer and B. Schwab, “A Comparison of Tree-Balancing Algorithms,”Comm. ACM,20:322–330 (1977).
R. Bayer and E. McCreight, “Organization and Maintenance of Large Ordered Indexes,”Acta Informatica,1:173–189 (1972).
D. Comer, “The Ubiquitous B-Tree,”Computing Surveys,11:121–137 (1979).
L. Guibas and R. Sedgewick, “A Dichromatic Framework for Balanced Trees,”Proceedings of the 19th IEEE FOCS Conference, pp. 8–21 (1978).
E. Horowitz and L. Sahni,Fundamentals of Data Structures (Computer Science Press, Rockville, Maryland, 1982).
P. L. Karlton, et al., “Performance of Height-Balance Trees,”Comm. ACM,19:23–28 (1976).
D. E. Knuth,The Art of Computer Programming Vol. 1 (Addison-Wesley, Reading, Mass., 1967).
D. E. Knuth,The Art of Computer Programming Vol. 3 (Addison-Wesley, Reading, Mass., 1973).
W. A. Martin and D. N. Ness, “Optimizing Binary Trees Grown With a Sorting Algorithm,”Comm. ACM,15:88–93 (1972).
R. E. Miller, N. Pippenger, A. L. Rosenberg, and L. Snyder, “Optimal 2–3 Trees,”SIAM J. Comp.,8:42–49 (1979).
J. Nieverselt and E. M. Reingold, “Binary Search Trees of Bounded Balance,”SIAM J. Comp.,2:33–43 (1973).
J. Nievergelt, “Binary Search Trees and File Organization,”Computing Survey,6:195–207 (1973).
A. Rosenberg and L. Snyder, “Minimal Comparison 2–3 Trees,”SIAM J. Comp.,7:465–480 (1978).
J. R. Van Doren, “An Asymptotic Analysis of Minimum OrderB-Trees,” Department of Computing and Information Sciences, Oklahoma State University, February, 1976.
A. C. Yao, “On Random 2–3 Trees,”Acta Informatica,9:159–170 (1978).
A. S. Zaki and J. L. Baer, “Query Costs inHB(1) Trees Versus 2–3 Trees,”Internat. J. Comp. Inform Sci.,6:383–395 (1981).
A. S. Zaki,Insertion and Search in 2–3 Trees Versus HB(1)Trees, Ph.D. Dissertation, University of Washington, Seattle, WA., 1977.
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Zaki, A.S. A comparative study of 2-3 trees and AVL trees. International Journal of Computer and Information Sciences 12, 13–33 (1983). https://doi.org/10.1007/BF00996801
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DOI: https://doi.org/10.1007/BF00996801