Towards optimal indexing for segment databases
Segment databases store N non-crossing but possibly touching segments in secondary storage. Efficient data structures have been proposed to determine all segments intersecting a vertical line (stabbing queries). In this paper, we consider a more general type of query for segment databases, determining intersections with respect to a generalized segment (a line, a ray, a segment) with a fixed angular coefficient. We propose two solutions to solve this problem. The first solution has optimal O(N/B) space complexity, where N is the database size and B is the page size, but the query time is far from optimal. The second solution requires O(N/B log2 B) space, the query time is O(logB N/B(logB N/B+log2 B+IL * (B))+T/B), which is very close to the optimal, and insertion amortized time is O(logB N/B+log2 B+1/Blog2 B N/B), where T is the size of the query result, and IL * (B) is a small constant, representing the number of times we must repeatedly apply the log* function to B before the result becomes ≤ 2.
KeywordsInternal Node Short Fragment Query Time Internal Memory Segment Tree
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- 1.L. Arge. The Buffer Tree: A New Technique for Optimal I/O Algorithms. In LNCS 955: Proc. of the 4th Int. Workshop on Algorithms and Data Structures, pages 334–345, 1995.Google Scholar
- 2.L. Arge, D.E. Vengroff, and J. S. Vitter. External-Memory Algorithms for Processing Line Segments in Geographic Information Systems. In Proc. of the 3rd Annual European Symp. on Algorithms, pages 295–310, 1995.Google Scholar
- 3.L. Arge and J. S. Vitter. Optimal Dynamic Interval Management in External Memory. In Proc. of the Int. Symp. on Foundations of Computer Science, pages 560–569, 1996.Google Scholar
- 4.E. Bertino, B. Catania, and B. Shidlovsky. Towards Optimal Indexing for Segment Databases. Extended version. Technical report, University of Milano, Italy, 1998.Google Scholar
- 10.A. Guttman. R-trees: A Dynamic Index Structure for Spatial Searching. In Proc. ACM SIGMOD Int. Conf. on Management of Data, pages 47–57, 1984.Google Scholar
- 11.C. Icking, R. Klein, and T. Ottmann. Priority Search Trees in Secondary Memory. In LNCS 314: Proc. of the Int. Workshop on Graph-Theoretic Concepts in Computer Science, pages 84–93, 1988.Google Scholar
- 18.J. Paredaens. Spatial Databases, the Final Frontier. In LNCS 893: Proc. of the 5th Int. Conf. on Database Theory, pages 14–31, 1995.Google Scholar
- 19.S. Ramaswamy and S. Subramanian. Path-Caching: A Technique for Optimal External Searching. In Proc. of the ACM Symp. on Principles of Database Systems, pages 25–35, 1994.Google Scholar
- 20.S. Ramaswamy. Efficient Indexing for Constraints and Temporal Databases. In LNCS 1186: Proc. of the 6th Int. Conf. on Database Theory, pages 419–431, 1997.Google Scholar
- 21.S. Subramanian and S. Ramaswamy. The P-Range Tree: A New Data Structure for Range Searching in Secondary Memory. In Proc. of the ACM-SIAM Symp. on Discrete Algorithms, pages 378–387, 1995.Google Scholar