Abstract
An almost complete (or 2-complete) tree is a binary search tree in which any two external nodes are no more than two levels apart. While complete binary search trees have an amortized update cost of Θ(n), we demonstrate that almost complete binary search trees have an amortized update cost of O(log2 n). Thus, they are an attractive alternative for those situations that require fast retrieval, that is, log n+O(1) comparisons, and have few updates.
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G. M. Adel'son-Vel'skii and E. M. Landis. An algorithm for the organization of information. Sov. Math. Dokl., 3:1259–1262, 1962.
A. Andersson. Improving partial rebuilding by using simple balance criteria. In Proceedings of the 1989 Workshop on Algorithms and Data Structures, pages 393–402. Springer-Verlag, 1989.
A. Andersson and T. W. Lai. Efficient maintenance of almost perfectly balanced trees. In preparation.
T. E. Gerasch. An insertion algorithm for a minimal internal path length binary search tree. Communications of the ACM, 31:579–585, 1988.
L. J. Guibas and R. Sedgewick. A dichromatic framework for balanced trees. In Proceedings of the 19th Annual IEEE Symposium on Foundations of Computer Science, pages 8–21, 1978.
T. W. Lai and D. Wood. Updating approximately complete trees. Technical Report CS-89-57, Univ. of Waterloo, 1989.
J. Nievergelt and E. M. Reingold. Binary search trees of bounded balance. SIAM Journal on Computing, 2:33–43, 1973.
M. H. Overmars. The Design of Dynamic Data Structures, volume 156 of Lecture Notes in Computer Science. Springer-Verlag, 1983.
M. H. Overmars and J. van Leeuwen. Dynamic multi-dimensional data structures based on quad-and k-d trees. Acta Informatica, 17:267–285, 1982.
Q. F. Stout and B. L. Warren. Tree rebalancing in optimal time and space. Communications of the ACM, 29:902–908, 1986.
J. van Leeuwen and D. Wood. Dynamization of decomposable searching problems. Information Processing Letters, 10:51–56, 1980.
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© 1990 Springer-Verlag Berlin Heidelberg
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Lai, T.W., Wood, D. (1990). Updating almost complete trees or one level makes all the difference. In: Choffrut, C., Lengauer, T. (eds) STACS 90. STACS 1990. Lecture Notes in Computer Science, vol 415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52282-4_42
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DOI: https://doi.org/10.1007/3-540-52282-4_42
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