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
Index Terms
- The point-range tree: a data structure for indexing intervals
Recommendations
Improved bounds for orthogonal point enclosure query and point location in orthogonal subdivisions in R3
SODA '15: Proceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithmsIn this paper, new results for two fundamental problems in the field of computational geometry are presented: orthogonal point enclosure query (OPEQ) in R3 and point location in orthogonal subdivisions in R3. All the results are in the pointer machine ...
Orthogonal range searching on the RAM, revisited
SoCG '11: Proceedings of the twenty-seventh annual symposium on Computational geometryWe present a number of new results on one of the most extensively studied topics in computational geometry, orthogonal range searching. All our results are in the standard word RAM model: We present two data structures for 2-d orthogonal range ...
Approximate colored range and point enclosure queries
In this paper, we formulate two classes of problems, the colored range query problems and the colored point enclosure query problems to model multi-dimensional range and point enclosure queries in the presence of categorical information. Many of these ...
Comments