Abstract
We provide a unifying framework for balanced binary trees in which we show how to ensure that insertions and deletions require a constant number of rotations or promotions. At the same time, the updating algorithms are also logarithmic in the worst case. We say that the updating algorithms have constant linkage cost.
The result provides insight into the constant linkage cost updating algorithms for red-black, red-h-black, and half-balanced trees. Moreover, it enables us to design new constant linkage cost updating algorithms for these as well as for other classes of trees. Specifically, we give constant linkage cost updating algorithms for α-balanced trees.
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References
G.M. Adel'son-Vel'skii and Y.M. Landis. An algorithm for the organization of information. Doklady Akademi Nauk, 146:263–266, 1962.
A. Andersson. Binary search trees of almost optimal height. Technical Report LU-CS-TR: 88:41, Department of Computer Science, Lund University, Lund, Sweden, 1988.
R. Bayer. Symmetric binary B-trees: Data structure and maintenance algorithms. Acta Informatica, 1:290–306, 1972.
R. Bayer and E.M. McCreight. Organization and maintenance of large ordered indexes. Acta Informatica, 1:173–189, 1972.
G. Frederickson and S. Rodger. A new approach to the dynamic maintenance of maximal points in the plane. In Proceedings of the 25th Annual Allerton Conference on Communication, Control, and Computing, pages 879–888, Urbana-Champaign, Illinois, 1987.
L.J. Guibas and R. Sedgewick. A dichromatic framework for balanced trees. In Proceedings of the 19th Annual Symposium on Foundations of Computer Science, pages 8–21, 1978.
Chr. Icking, R. Klein, and Th. Ottmann. Priority search trees in secondary memory. In Graphtheoretic Concepts in Computer Science (WG '87), Staffelstein, Lecture Notes in Computer Science 314, pages 84–93, 1987.
E.M. McCreight. Priority search trees. SIAM Journal on Computing, 14:257–276, 1985.
H. J. Olivié. A Study of Balanced Binary Trees and Balanced One-Two Trees. PhD thesis, Departement Wiskunde, Universiteit Antwerpen, Antwerp, Belgium, 1980.
H. J. Olivié. A new class of balanced search trees: Half-balanced search trees. RAIRO Informatique théorique, 16:51–71, 1982.
N. Sarnak and R. E. Tarjan. Planar point location using persistent search trees. Communications of the ACM, 29:669–679, 1986.
R.E. Tarjan. Updating a balanced search tree in O(1) rotations. Information Processing Letters, 16:253–257, 1983.
J. van Leeuwen and M. Overmars. Stratified balanced search trees. Acta Informatica, 18:345–359, 1983.
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© 1990 Springer-Verlag Berlin Heidelberg
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Ottmann, T., Wood, D. (1990). How to update a balanced binary tree with a constant number of rotations. In: Gilbert, J.R., Karlsson, R. (eds) SWAT 90. SWAT 1990. Lecture Notes in Computer Science, vol 447. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52846-6_83
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DOI: https://doi.org/10.1007/3-540-52846-6_83
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Online ISBN: 978-3-540-47164-6
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