Moez Chaabouni
ABSTRACT
In this paper, we propose a data structure, the Point-Range Tree (PR-Tree), specifically designed for indexing intervals. With the PR-Tree, a point data can be queried against a set of intervals to determine which of those intervals overlap the point. The PR-tree allows dynamic insertions and deletions while it maintains itself balanced. A balanced PR-Tree takes Ο(log n) time for search. Insertion, deletion, and storage space have worst case requirements of Ο(n log n + m), Ο(n log2 n + m), and Ο(n log n), respectively, where n is the total number of intervals in the tree, and m the number of nodes visited during insertion and deletion. A modified version of the PR-Tree is also developed to minimize space usage. An additional advantage of the PR-Tree is that it can be easily extended to multi-dimensional domains.
- 1.Adel'son-Vel'skii G. M. and Landis E. M., "An Algorithm for the Organization of Information," Soviet Math. Dokl., 8, 1962.Google Scholar
- 2.Chssbouni M., "Design of a Top Level index for s Discrimination Network Used in a Database Rule System," Master Thesis, Department of Computer Science and Engineering, Wright State University, April 1990.Google Scholar
- 3.Guttmem A., "R-Trees: A Dynamic Index Structure for Spatied Searching," Proceedings of the 1984 ACM-SIGMOD Conference, pp. ~7-57, June 1984. Google ScholarDigital Library
- 4.Hanson E. N., "An Initial Report on the Design of Ariel: A DBMS with an Integrated Production Rule System," SIGMOD Record, I8(8), pp. IP.- 19, September 1989. Google ScholarDigital Library
- 5.Hanson E. N., '~rhe Interval Skip List: A Data Structure for Finding All Intervals That Overlap a Point," Proceedings of the 1991 Workshop on Algorithms and Data Strectures.Google Scholar
- 6.Hanson E. N. and Chaabouni M., "The IBS-Tree: A Data Structure for Finding All Intervals that Overlap a Point,~ Technical Report WSU- C$-90- II, Department of Compwter Science and Engineering, Wright State University, April 1990.Google Scholar
- 7.Hanson E. N., Chaabouni M., Kim C. H., and Wang Y. W., "A Predicate Matching Algorithm for Database Rule Systems," Proceedings of the 1990 A CM-SIGMOD Conference, pp. ~71-~80, May 1990. Google ScholarDigital Library
- 8.McCreight E. M., ~Priority Search Trees," SIAM J. COMPUT. 1~(~), pp. ~57-~76, May 1985.Google Scholar
- 9.Pugh W., "A Skip List Cookbook," Technical Report CS-TR-~.86, Department of Computer Science, Universi~ of Maryland, July 1989. Google ScholarDigital Library
- 10.Pugh W., "Skip Lists: A Probabilistic Alternative to Balanced Trees," Communications of the A CM, 33(6), pp. 668-676, June 1990. Google ScholarDigital Library
- 11.Samet H., The Design and Analysis of Spatial Data Structures. Addison Wesley, 1990. Google ScholarDigital Library
- 12.Wirth N., Algorithms and Data Structures. Prentice-Hall, 1986. Google ScholarDigital Library
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