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Access Methods for Intervals

  • Yannis Manolopoulos
  • Yannis Theodoridis
  • Vassilis J. Tsotras
Part of the Advances in Database Systems book series (ADBS, volume 17)

Abstract

Intervals provide a compact way to represent the duration of a property. They appear in many database applications, including spatial, temporal [Jensen and Snodgrass, 1999], constraint [Bertino et al., 1997; Ramaswamy, 1997] and object-oriented databases [Kanellakis et al., 1993]. Due to their importance, many techniques have been proposed in literature for indexing intervals. Here we concentrate on the 1-dimensional dynamic interval management problem and in particular the so-called stabbing query. We first present classical main-memory solutions to the stabbing query, namely: the Interval Tree, the Segment Tree and the Priority Search Tree. These structures have been extended in various ways to support intervals in external memory (i.e., on the disk). Among other structures in this chapter we discuss: the Segment R-tree, the External Segment Tree, the External Priority Search Tree, the Metablock Tree, the External Memory Interval Tree, the Binary-Blocked Interval Tree and the Time-Polygon Index.

Keywords

Internal Node Query Point Query Time External Memory Access Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Arge, L. and Vitter, J.S. (1996). Optimal Dynamic Interval Management in External Memory. In Proceedings of the 37 th IEEE Symposium on Foundations of Computer Science, pages 560–569.Google Scholar
  2. Blankenagel, G. and Gueting, R.H. (1990). XP-trees: External Priority Search Trees. Technical Report, Informatik-Bericht No.92, Fern Universitaet Hagen.Google Scholar
  3. Blankenagel, G. and Gueting, R.H. (1994). External Segment Trees. Algorithmica, 12(6):498–532.MathSciNetCrossRefGoogle Scholar
  4. Becker, B., Gschwind, S., Ohler, T., Seeger, B., and Widmayer, P. (1996). An Asymptotically Optimal Multiversion B-tree. The VLDB Journal, 5(4):264–275.CrossRefGoogle Scholar
  5. Bentley, J.L. (1977). Algorithms for Klee’s Rectangle Problems. Computer Science Department, Carnegie-Mellon University, Pittsburgh.Google Scholar
  6. Bertino, E., Catania, B., and Shidlovski, B. (1997). Towards Optimal Two-dimensional Indexing for Constraint Databases. Information Processing Letters, 64(1):1–8.MathSciNetCrossRefGoogle Scholar
  7. Chiang, Y.-J. and Silva, C.T. (1999). External Memory Techniques for Isosurface Extraction in Scientific Visualization. In External Memory Algorithms and Visualization, by Abello, J. and Vitter, J.S. (Eds.), to appear. American Mathematical Society, AMS-DIMACS Book Series.Google Scholar
  8. Chiang, Y.-J. and Tamassia, R. (1992). Dynamic Algorithms in Computational Geometry. In Proceedings of the IEEE (special issue on Computational Geometry), 80(9):362–381.Google Scholar
  9. Cormen, T.H., Leiserson, C.E., and Rivest, R.L. (1990). Introduction to Algorithms. MIT Press.Google Scholar
  10. Edelsbrunner, H. (1983). A New Approach to Rectangle Intersections, Part I&II. International Journal of Computer Mathematics, 13:209–229.MathSciNetzbMATHCrossRefGoogle Scholar
  11. Gaede, V. and Guenther, O. (1998). Multidimensional Access Methods. A CM Computing Surveys, 30(2):170–231.CrossRefGoogle Scholar
  12. Gutrman, A. (1984). R-trees: a Dynamic Index Structure for Spatial Searching. In Proceedings of ACM SIGMOD Conference on Management of Data, pages 47–57.Google Scholar
  13. Hellerstein, J.M., Koutsoupias, E., and Papadimitriou, C.H. (1997). On the Analysis of Indexing Schemes. In Proceedings of the 16 th ACM Symposium on Principles of Database Systems, pages 249–256.Google Scholar
  14. Icking, C., Klein, R., and Ottmann, T. (1988). Priority Search Trees in Secondary Memory. In Graph Theoretic Concepts in Computer Science, pages 84–93. Springer Verlag LNCS 314.Google Scholar
  15. Jensen, C.S. and Snodgrass, R.T. (1999). Temporal Data Management. IEEE Transactions on Knowledge and Data Engineering, 11(1):36–44.CrossRefGoogle Scholar
  16. Kanellakis, P., Ramaswamy, S., Vengroff, D., and Vitter, J.S. (1993). Indexing for Data Models with Constraint and Classes. In Proceedings of the 12 th ACM Symposium on Principles of Database Systems, pages 233–243.Google Scholar
  17. Kolovson, C. and Stonebraker, M. (1991). Segment Indexes: Dynamic Indexing Techniques for Multi-dimensional Interval Data. In Proceedings of ACM SIGMOD Conference on Management of Data, pages 138–147.Google Scholar
  18. Kumar, A., Tsotras, V.J., and Faloutsos, C. (1995). Access Methods for Bitemporal Databases. In Recent Advances in Temporal Databases, by Clifford, J. and Tuzhilin, A. (eds.), pages 235–254. Springer-Verlag.Google Scholar
  19. McCreight, E.M. (1985). Priority Search Trees. SIAM Journal of Computing, 14(2):257–276.MathSciNetzbMATHCrossRefGoogle Scholar
  20. Mehlhorn, K. (1984). Data Structures and Efficient Algorithms, Vol.3: Multi-dimensional Searching and Computational Geometry. Springer Verlag, EATCS Monographs.Google Scholar
  21. Nascimento, M., Dunham, M.H., and Kouramajian, V. (1996). A Multiple Tree Mapping-based Approach for Valid-Time Ranges. Journal of the Brazilian Computer Society, 2(3):36–46.Google Scholar
  22. Ramaswamy, S. (1997). Efficient Indexing for Constraint and Temporal Databases. In Proceedings of the 6 th International Conference on Database Theory, pages 419–431.Google Scholar
  23. Ramaswamy, S. and Subramanian, S. (1994). Path Caching: a Technique for Optimal External Searching. In Proceedings of the 13 rd ACM Symposium on Principles of Database Systems, pages 25–35.Google Scholar
  24. Salzberg, B. and Tsotras, V.J. (1999). A Comparison of Access Methods for Time-Evolving Data. ACM Computing Surveys, to appear. Also available as TimeCenter TR-18, http:// www.cs.auc.dk/research/DBS/tdb/TimeCenter/publications2.htmlGoogle Scholar
  25. Samet, H. (1990). The Design and Analysis of Spatial Data Structures. Addison-Wesley.Google Scholar
  26. Shen, H., Ooi, B.C., and Lu, H. (1994). The TP-Index: a Dynamic and Efficient Indexing Mechanism for Temporal Databases. In Proceedings of the 10 th IEEE International Conference on Data Engineering, pages 274–281.Google Scholar
  27. Subramanian, S. and Ramaswamy, S. (1995). The P-range Tree: a New Data Structure for Range Searching in Secondary Memory. In Proceedings of the 6 th ACM-SIAM Symposium on Discrete Algorithms, pages 378–387.Google Scholar
  28. Tsotras, V.J. and Kangelaris, N. (1995). The Snapshot Index: an I/O-Optimal Access Method for Timeslice Queries. Information Systems, 20(3):237–260.CrossRefGoogle Scholar
  29. Vitter, J.S. (1998). External Memory Algorithms. In Proceedings of the 17 th ACM Symposium on Principles of Database Systems, pages 119–128.Google Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Yannis Manolopoulos
    • 1
  • Yannis Theodoridis
    • 2
  • Vassilis J. Tsotras
    • 3
  1. 1.Aristotle UniversityGreece
  2. 2.Greece
  3. 3.University of CaliforniaRiversideUSA

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