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.
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References
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.
Blankenagel, G. and Gueting, R.H. (1990). XP-trees: External Priority Search Trees. Technical Report, Informatik-Bericht No.92, Fern Universitaet Hagen.
Blankenagel, G. and Gueting, R.H. (1994). External Segment Trees. Algorithmica, 12(6):498–532.
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.
Bentley, J.L. (1977). Algorithms for Klee’s Rectangle Problems. Computer Science Department, Carnegie-Mellon University, Pittsburgh.
Bertino, E., Catania, B., and Shidlovski, B. (1997). Towards Optimal Two-dimensional Indexing for Constraint Databases. Information Processing Letters, 64(1):1–8.
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.
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.
Cormen, T.H., Leiserson, C.E., and Rivest, R.L. (1990). Introduction to Algorithms. MIT Press.
Edelsbrunner, H. (1983). A New Approach to Rectangle Intersections, Part I&II. International Journal of Computer Mathematics, 13:209–229.
Gaede, V. and Guenther, O. (1998). Multidimensional Access Methods. A CM Computing Surveys, 30(2):170–231.
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.
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.
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.
Jensen, C.S. and Snodgrass, R.T. (1999). Temporal Data Management. IEEE Transactions on Knowledge and Data Engineering, 11(1):36–44.
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.
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.
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.
McCreight, E.M. (1985). Priority Search Trees. SIAM Journal of Computing, 14(2):257–276.
Mehlhorn, K. (1984). Data Structures and Efficient Algorithms, Vol.3: Multi-dimensional Searching and Computational Geometry. Springer Verlag, EATCS Monographs.
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.
Ramaswamy, S. (1997). Efficient Indexing for Constraint and Temporal Databases. In Proceedings of the 6 th International Conference on Database Theory, pages 419–431.
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.
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.html
Samet, H. (1990). The Design and Analysis of Spatial Data Structures. Addison-Wesley.
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.
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.
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.
Vitter, J.S. (1998). External Memory Algorithms. In Proceedings of the 17 th ACM Symposium on Principles of Database Systems, pages 119–128.
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Manolopoulos, Y., Theodoridis, Y., Tsotras, V.J. (2000). Access Methods for Intervals. In: Advanced Database Indexing. Advances in Database Systems, vol 17. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-8590-3_4
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DOI: https://doi.org/10.1007/978-1-4419-8590-3_4
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