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Multidimensional Balanced Binary Trees
July 1989 (vol. 38 no. 7)
pp. 968-985
ASCII Text
x 
 
V.K. Vaishnavi, "Multidimensional Balanced Binary Trees," IEEE Transactions on Computers, vol. 38, no. 7, pp. 968-985, July, 1989.
 
 
BibTex
x
 
@article{ 10.1109/12.30849,
author = {V.K. Vaishnavi},
title = {Multidimensional Balanced Binary Trees},
journal ={IEEE Transactions on Computers},
volume = {38},
number = {7},
issn = {0018-9340},
year = {1989},
pages = {968-985},
doi = {http://doi.ieeecomputersociety.org/10.1109/12.30849},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - Multidimensional Balanced Binary Trees
IS - 7
SN - 0018-9340
SP968
EP985
EPD - 968-985
A1 - V.K. Vaishnavi,
PY - 1989
KW - balanced multidimensional tree structure; k-dimensional balanced binary tree; positive integer; data structure; access; insertion; deletion; data structures; trees (mathematics).
VL - 38
JA - IEEE Transactions on Computers
ER -
 
A new balanced multidimensional tree structure called a k-dimensional balanced binary tree, where k is a positive integer, is presented and integrated. It is shown that the data structure can be used to manage a set of n k-dimensional data items such that access, insertion, and deletion operations can be supported in O(log n+k) time. The data structure is a multidimensional generalization of a

[1] R. Bayer, "Symmetric binary B-trees: Data structure and maintenance algorithms,"Acta Informatica, vol. 1, pp. 290-306, 1972.
[2] S. W. Bent, D. D. Sleator, and R. E. Tarjan, "Biased search trees,"SIAM J. Comput., vol. 14, pp. 545-568, 1985.
[3] J. L. Bentley and J. B. Saxe, "Algorithms on vector sets,"SIGACT News, vol. 11, pp. 36-39, 1979.
[4] J. R. Driscoll, N. Sarnak, D. D. Sleator, and R. E. Tarjan, "Making data structures persistent," inProc. 28th Annu. Symp. Theory Comput., 1986, pp. 109-120.
[5] J. Feigenbaum and R. E. Tarjan, "Two new kinds of biased search trees,"Bell Syst. Tech. J., vol. 62, pp. 3139-3158, 1983.
[6] R. H. Gueting and H. P. Kriegel, "Multidimensional B-trees: An efficient dynamic file structure for exact match queries," inProc. 10th GI Annu. Conf., Informatik Fachberichte. Springer-Verlag, 1980, pp. 375-388.
[7] R. H. Gueting and H. P. Kriegel, "Dynamic k-dimensional multiway search under time-varying frequencies," inProc. 5th GI Conf. Theoret. Comput. Sci., Lecture Notes in Computer Science, vol. 104, pp. 135-145, 1981.
[8] K. Mehlhorn, "Dynamic binary search trees,"SIAM J. Comput., vol. 8, pp. 175-198, 1979.
[9] H. Olive, "A new class of balanced search trees: Half-balanced binary trees," Tech. Rep. 80-02, Interstedelijke Industriele Hogeschool Antwerpen-Mechlen, Antwerp, 1980.
[10] R. E. Tarjan, "Updating a balanced search tree in 0(1) rotations,"Inform. Proc. Lett., vol. 16, pp. 253-257, 1983.
[11] R. Endre Tarjan,Data Structures and Network Algorithms, Society for Industrial and Applied Mathematics, 1983.
[12] A. K. Tsakalidis, " An optimal implementation for localized search," Tech. Rep. A 84/06, Univ. of Sarlandes, West Germany, 1984.
[13] V. K. Vaishnavi, "Multidimensional height-balanced trees,"IEEE Trans. Comput., vol. C-33, pp. 334-343, 1984.
[14] V. K. Vaishnavi, "On the height of multidimensional height-balanced trees,"IEEE Trans. Comput., vol. C-35, pp. 773-780, 1986.
[15] V. K. Vaishnavi, "Weighted leaf AVL-trees,"SIAM J. Comput., vol. 16, pp. 503-537, 1987.

Index Terms:
balanced multidimensional tree structure; k-dimensional balanced binary tree; positive integer; data structure; access; insertion; deletion; data structures; trees (mathematics).
Citation:
V.K. Vaishnavi, "Multidimensional Balanced Binary Trees," IEEE Transactions on Computers, vol. 38, no. 7, pp. 968-985, July 1989, doi:10.1109/12.30849
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