This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Range Aggregate Processing in Spatial Databases
December 2004 (vol. 16 no. 12)
pp. 1555-1570
A range aggregate query returns summarized information about the points falling in a hyper-rectangle (e.g., the total number of these points instead of their concrete ids). This paper studies spatial indexes that solve such queries efficiently and proposes the aggregate Point-tree (aP-tree), which achieves logarithmic cost to the data set cardinality (independently of the query size) for two-dimensional data. The aP-tree requires only small modifications to the popular multiversion structural framework and, thus, can be implemented and applied easily in practice. We also present models that accurately predict the space consumption and query cost of the aP-tree and are therefore suitable for query optimization. Extensive experiments confirm that the proposed methods are efficient and practical.

[1] L. Arge, “External Memory Data Structures,” Handbook of Massive Data Sets, J. Abello, P.M. Pardalos, M.G.C. Resende, eds., pp. 313-357, Kluwer Academic Publishers, 2002.
[2] L. Arge, “The Buffer Tree: A New Technique for Optimal I/O-Algorithms,” Proc. Workshop Algorithms and Data Structures, 1995.
[3] S. Acharya, V. Poosala, and S. Ramaswamy, “Selectivity Estimation in Spatial Databases,” Proc. SIGMOD Conf., 1999.
[4] P. Agarwal, L. Arge, J. Yang, and K. Yi, “I/O-Efficient Structures for Orthogonal Range Max and Stabbing Max,” Proc. European Space Agency Conf., 2003.
[5] L. Arge and J. Vahrenhold, “I/O-Efficient Dynamic Planar Point Location,” Proc. ACM Symp. Computational Geometry, 2000.
[6] A. Belussi and C. Faloutsos, “Estimating the Selectivity of Spatial Queries Using the Correlation's Fractal Dimension,” Proc. Very Large Databases Conf., 1995.
[7] B. Becker, S. Gschwind, T. Ohler, B. Seeger, and P. Widmayer, “An Asymptotically Optimal Multiversion B-Tree,” Very Large Databases J., vol. 5, no. 4, pp. 264-275, 1996.
[8] B. Beckmann, H. Kriegel, R. Schneider, and B. Seeger, “The R*-Tree: An Efficient and Robust Access Method,” Proc. SIGMOD Conf., 1990.
[9] J. Bercken, B. Seeger, and P. Widmayer, “A Generic Approach to Bulk Loading Multidimensional Index Structures,” Proc. Very Large Databases Conf., 1997.
[10] C. Chung, S. Chun, J. Lee, and S. Lee, “Dynamic Update Cube for Range-Sum Queries,” Proc. Very Large Databases Conf., 2001.
[11] C. Chan and Y. Ioannidis, “Hierarchical Cubes for Range-Sum Queries,” Proc. Very Large Databases Conf. , 1999.
[12] M. Denny, M. Franklin, P. Castro, and A. Purakayastha, “Mobiscope: A Scalable Spatial Discovery Service for Mobile Network Resources,” Mobile Data Management, 2003.
[13] J. Driscoll, N. Sarnak, D. Sleator, and R. Tarjan, “Making Data Structures Persistent,” J. Computer and System Sciences, vol. 38, no. 1, pp. 86-124, 1989.
[14] C. Faloutsos and I. Kamel, “Beyond Uniformity and Independence: Analysis of R-trees Using the Concept of Fractal Dimension,” ACM Symp. Principles of Database Systems, pp. 4-13, 1994.
[15] A. Guttman, “R-Trees: A Dynamic Index Structure for Spatial Searching,” Proc. SIGMOD Conf., 1984.
[16] S. Govindarajan, P. Agarwal, and L. Arge, “CRB-Tree: An Efficient Indexing Scheme for Range Aggregate Queries,” Proc. Int'l Conf. Database Theory, 2003.
[17] S. Geffner, A. Agrawal, A. Abbadi, and T. Smith, “Relative Prefix Sums: An Efficient Approach for Querying Dynamic OLAP Data Cubes,” Proc. Int'l Conf. Data Eng., 2000.
[18] J. Gray, A. Bosworth, A. Layman, and H. Pirahesh, “Data Cube: A Relational Aggregation Operator Generalizing Group-By, Cross-Tabs and Subtotals,” Proc. Int'l Conf. Data Eng., 1996.
[19] D. Gunopulos, G. Kollios, V. Tsotras, and C. Domeniconi, “Approximate Multi-Dimensional Aggregate Range Queries over Real Attributes,” Proc. SIGMOD Conf., 2000.
[20] C. Ho, R. Agrawal, N. Megiddo, and R. Srikant, “Range Queries in OLAP Data Cubes,” Proc. SIGMOD Conf., 1997.
[21] M. Jurgens and H. Lenz, “The Ra*-Tree: An Improved R-Tree with Materialized Data for Supporting Range Queries on OLAP-Data,” Proc. DEXA Workshop, 1998.
[22] M. Jurgens and H. Lenz, “PISA: Performance Models for Index Structures with and without Aggregated Data,” Proc. Int'l Conf. Statistical and Scientific Database Management, 1999.
[23] I. Kamel and C. Faloutsos, “On Packing R-Trees,” Proc. Int'l Conf. Information and Knowledge Management, 1993.
[24] G. Kollios, D. Gunopulos, V. Tsotras, A. Delis, and M. Hadjieleftheriou, “Indexing Animated Objects Using Spatiotemporal Access Methods,” IEEE Trans. Knowledge and Data Eng., vol. 13, no. 5, pp. 758-777, Sept./Oct. 2001.
[25] A. Kumar, V. Tsotras, and C. Faloutsos, “Design Access Methods for Bi-temporal Databases,” IEEE Trans. Knowledge and Data Eng., vol. 10, no. 1, pp. 1-20, Jan./Feb. 1998.
[26] I. Lazaridis and S. Mehrotra, “Progressive Approximate Aggregate Queries with a MultiResolution Tree Structure,” Proc. SIGMOD Conf., 2001.
[27] M. Muralikrishna and D. DeWitt, “Equi-Depth Histograms for Estimating Selectivity Factors for MultiDimensional Queries,” Proc. SIGMOD Conf., 1988.
[28] Y. Poosala and Y. Ioannidis, “Selectivity Estimation without the Attribute Value Independence Assumption,” Proc. Very Large Databases Conf., 1997.
[29] D. Papadias, P. Kalnis, J. Zhang, and Y. Tao, “Efficient OLAP Operations in Spatial Data Warehouses,” Proc. Symp. Spatial and Temporal Databases, 2001.
[30] M. Riedewald, D. Agrawal, and A. Abbadi, “Efficient Integration and Aggregation of Historical Information,” Proc. SIGMOD Conf., 2002.
[31] T. Sellis, N. Roussopoulos, and C. Faloutsos, “The R+-Tree: A Dynamic Index for MultiDimensional Objects,” Proc. Very Large Databases Conf., 1987.
[32] B. Salzberg and V. Tsotras, “A Comparison of Access Methods for Temporal Data,” ACM Computing Surveys, vol. 31, no. 2, pp. 158-221, 1999.
[33] Y. Tao and D. Papadias, “The MV3R-Tree: A Spatio-Temporal Access Method for Timestamp and Interval Queries,” Proc. Very Large Databases Conf., 2001.
[34] Y. Tao, D. Papadias, and J. Zhang, “Efficient Cost Models for Overlapping and MultiVersion Structures,” ACM Trans. Database Systems, vol. 27, no. 3, pp. 299-342, 2002.
[35] Y. Theodoridis and T. Sellis, “A Model for the Prediction of R-tree Performance,” Proc. Symp. Principles of Database Systems, 1996.
[36] P. Varman and R. Verma, “An Efficient Multiversion Access Structure,” IEEE Trans. Knowledge and Data Eng., vol. 9, no. 3, pp. 391-409, May/June 1997.
[37] J. Vitter and M. Wang, “Approximate Computation of Multidimensional Aggregates of Sparse Data Using Wavelets,” Proc. SIGMOD Conf., 1999.
[38] A. Yao, “Random 2-3 Trees,” Acta Informatica, vol. 2, no. 9, pp. 159-179, 1978.
[39] J. Yang and J. Widom, “Incremental Computation and Maintenance of Temporal Aggregates,” Proc. Int'l Conf. Data Eng., 2001.
[40] D. Zhang, A. Markowetz, V. Tsotras, D. Gunopulos, and B. Seeger, “Efficient Computation of Temporal Aggregates with Range Predicates,” Proc. Symp. Principles of Database Systems, 2001.
[41] D. Zhang, V. Tsotras, and D. Gunopulos, “Efficient Aggregation over Objects with Extent,” Proc. Symp. Principles of Database Systems, 2002.

Index Terms:
Database, spatial database, range queries, aggregation.
Citation:
Yufei Tao, Dimitris Papadias, "Range Aggregate Processing in Spatial Databases," IEEE Transactions on Knowledge and Data Engineering, vol. 16, no. 12, pp. 1555-1570, Dec. 2004, doi:10.1109/TKDE.2004.93
Usage of this product signifies your acceptance of the Terms of Use.