Abstract
Database applications very often require a sophisticated class of storage structures in order to answer different types of queries efficiently. This often dictates that the file should be organized on multiple keys. Several storage structures have been proposed to satisfy these needs. Most of these are a generalization of the storage structures used for managing one-dimensional data. Thek-d tree is one such example and it is a natural generalization of the standard one-dimensional binary search tree. Recently, a new storage structure, called theBD tree, was proposed to manage multidimensional data. This structure has good dynamic characteristics. Several variations are possible on the basick-d tree structure. This paper studies the performance implications of three variations. Further, it provides an empirical performance comparison of thek-d tree andBD tree in database applications.
Similar content being viewed by others
References
R. Rivest, Partial-Match Retrieval Algorithms,SIAM J. Comput.,5(1):19–50 (March 1976).
J. L. Bentley and M. I. Shamos, A Problem in Multivariate Statistics: Algorithm, Data Structure and Applications,15th Allerton Conf. on Communication, Control, and Computing, pp. 193–201 (1977).
J. L. Bentley, Multidimensional Divide- and-Conquer,CACM,23(4):214–228 (April 1980).
M. L. Fredman, A Lower Bound on the Complexity of Orthogonal Range Queries,J. ACM,28(4):696–705 (1981).
J. L. Bentley and H. A. Maurer, Efficient Worst-Case Data Structures for Range Searching,Acta Information, Vol. 13, pp. 155–168 (1980).
G. S. Lueker and D. E. Willard, A Data Structure for Dynamic Range Queries,Inf. Processing Letters,5(5):209–213 (December 1982).
D. E. Willard, New Data Structures for Orthogonal Range Queries,SIAM J. Comp.,14(1):232–253 (1985).
D. T. Lee and C. K. Wong, Quintary Trees: A File Structure for Multidimensional Database Systems,ACM Trans. Database Syst.,5(3):339–353 (September 1980).
J. L. Bentley, Multidimensional Binary Search Trees Used for Associative Searching,CACM,18(9):509–517 (September 1975).
J. L. Bentley, Multidimensional Binary Search Trees in Database Applications,IEEE Trans. Software Eng.,SE-5(4):333–340 (July 1979).
J. Orenstein, Multidimensional Tries Used for Associative Searching,Info. Processing Letters,14(4):150–157 (1982).
S. P. Dandamudi, Storage Structures for Main Memory Based Database Systems, M.Sc. thesis, Department of Computational Science, University of Saskatchewan, Saskatoon (1984).
S. P. Dandamudi and P. G. Sorenson, Performance of a Modifiedk-d Tree, Tech. Rep. 84-10, Department of Computational Science, University of Saskatchewan, Saskatoon (1984).
Y. Ohsawa and M. Sakauchi, TheBD-Tree—A NewN-Dimensional Data Structure With Highly Efficient Dynamic Characteristics,IFIP Conf., Paris, pp. 539–544 (1983).
D. T. Lee and C. K. Wong, Worst Case Analysis for Region and Partial Region Searches in Multidimensional Binary Search Trees and Balanced Quad Trees,Acta Informatica,9:23–29 (1977).
J. L. Bentley and W. A. Burkhard, Heuristics for Partial Match Retrieval Data Base Design,Info. Processing Letters,4(5):132–135 (February 1976).
J. H. Friedman, J. L. Bentley, and R. A. Finkel, An Algorithm for Finding Best Matches in Logarithmic Expected Time,ACM Trans. Math. Software,3(3):209–226 (September 1977).
S. P. Dandamudi and P. G. Sorenson, Algorithms for theBD Tree Structure, Tech. Rep. 84-11, Department of Computational Science, University of Saskatchewan, Saskatoon (1984).
D. Comer, The UbiquitousB-Tree,ACM Comput. Surv.,11(2):121–137 (June 1979).
D. E. Knuth,The Art of Computer Programming, Vol. 3: Sorting and Searching, Addison-Wesley, Reading (1973).
J. Nievergelt, H. Hinterberger, and K. C. Sevcik, The Grid File: An Adaptable, Symmetric Multikey File Structure,ACM Trans. Database Systems,9(1):38–71 (March 1984).
H. P. Kriegel, Performance Comparison of Index Structures for Multikey Retrieval,Proc. ACM SIGMOD 1984, Boston, pp. 186–196 (1984).
S. Christodoulakis, Estimating Selectivities in Data Bases, Ph.D. thesis, Department of Computer Science, University of Toronto (1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dandamudi, S.P., Sorenson, P.G. An empirical performance comparison of some variations of thek-d Tree andBD tree. International Journal of Computer and Information Sciences 14, 135–159 (1985). https://doi.org/10.1007/BF00991003
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00991003