Closest pair queries in spatial databases

ABSTRACT

This paper addresses the problem of finding the K closest pairs between two spatial data sets, where each set is stored in a structure belonging in the R-tree family. Five different algorithms (four recursive and one iterative) are presented for solving this problem. The case of 1 closest pair is treated as a special case. An extensive study, based on experiments performed with synthetic as well as with real point data sets, is presented. A wide range of values for the basic parameters affecting the performance of the algorithms, especially the effect of overlap between the two data sets, is explored. Moreover, an algorithmic as well as an experimental comparison with existing incremental algorithms addressing the same problem is presented. In most settings, the new algorithms proposed clearly outperform the existing ones.

REFERENCES

• 1: Norbert Beckmann , Hans-Peter Kriegel , Ralf Schneider , Bernhard Seeger, The R*-tree: an efficient and robust access method for points and rectangles, Proceedings of the 1990 ACM SIGMOD international conference on Management of data, p.322-331, May 23-26, 1990, Atlantic City, New Jersey, United States
• 2: Kevin S. Beyer , Jonathan Goldstein , Raghu Ramakrishnan , Uri Shaft, When Is ''Nearest Neighbor'' Meaningful?, Proceeding of the 7th International Conference on Database Theory, p.217-235, January 10-12, 1999
• 3: Thomas Brinkhoff , Hans-Peter Kriegel , Bernhard Seeger, Efficient processing of spatial joins using R-trees, Proceedings of the 1993 ACM SIGMOD international conference on Management of data, p.237-246, May 25-28, 1993, Washington, D.C., United States
• 4: Antonio Corral , Michael Vassilakopoulos , Yannis Manolopoulos, Algorithms for Joining R-Trees and Linear Region Quadtrees, Proceedings of the 6th International Symposium on Advances in Spatial Databases, p.251-269, July 20-23, 1999
• 5: A. Corral, Y. Manolopoulos, Y. Theodoridis and M. Vassilakopoulos: "Closest Pair Queries in Spatial Databases", Technical Report, Data Engineering Lab, Dept. of Informatics, Aristotle Univ. of Thessaloniki, Greece, 1999 (available from URL: http://delab, csd. auth. gr/#michalis/cpq, html).
• 6: David J. DeWitt , Navin Kabra , Jun Luo , Jignesh M. Patel , Jie-Bing Yu, Client-Server Paradise, Proceedings of the 20th International Conference on Very Large Data Bases, p.558-569, September 12-15, 1994
• 7: Martin Dietzfelbinger , Torben Hagerup , Jyrki Katajainen , Martti Penttonen, A reliable randomized algorithm for the closest-pair problem, Journal of Algorithms, v.25 n.1, p.19-51, Oct. 1997 [doi>10.1006/jagm.1997.0873]
• 8: Volker Gaede , Oliver Günther, Multidimensional access methods, ACM Computing Surveys (CSUR), v.30 n.2, p.170-231, June 1998 [doi>10.1145/280277.280279]
• 9: M.T. Goodrich, J.-J. Tsay, D.E. Vengroff and J.S. Vitter: "External-Memory Computational Geometry", Proc. 3#th Annual IEEE Syrup. on Foundations of Comp. Science (FOCS'93), pp.714- 723, Palo Alto, CA, 1993.
• 10: Antonin Guttman, R-trees: a dynamic index structure for spatial searching, Proceedings of the 1984 ACM SIGMOD international conference on Management of data, June 18-21, 1984, Boston, Massachusetts
• 11: Gísli R. Hjaltason , Hanan Samet, Incremental distance join algorithms for spatial databases, Proceedings of the 1998 ACM SIGMOD international conference on Management of data, p.237-248, June 01-04, 1998, Seattle, Washington, United States
• 12: Samir Khuller , Yossi Matias, A simple randomized sieve algorithm for the closest-pair problem, Information and Computation, v.118 n.1, p.34-37, April 1995 [doi>10.1006/inco.1995.1049]
• 13: Scott T. Leutenegger , Mario A. Lopez, The Effect of Buffering on the Performance of R-Trees, Proceedings of the Fourteenth International Conference on Data Engineering, p.164-171, February 23-27, 1998
• 14: Nikos Mamoulis , Dimitris Papadias, Integration of spatial join algorithms for processing multiple inputs, Proceedings of the 1999 ACM SIGMOD international conference on Management of data, p.1-12, May 31-June 03, 1999, Philadelphia, Pennsylvania, United States
• 15: Yannis Manolopoulos , Yannis Theodoridis , Vassilis J. Tsotras, Advanced database indexing, Kluwer Academic Publishers, Norwell, MA, 2000
• 16: Dimitris Papadias , Nikos Mamoulis , Yannis Theodoridis, Processing and optimization of multiway spatial joins using R-trees, Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems, p.44-55, May 31-June 03, 1999, Philadelphia, Pennsylvania, United States [doi>10.1145/303976.303981]
• 17: Apostolos Papadopoulos , Yannis Manolopoulos, Performance of Nearest Neighbor Queries in R-Trees, Proceedings of the 6th International Conference on Database Theory, p.394-408, January 08-10, 1997
• 18: Apostolos Papadopoulos , Yannis Manolopoulos, Nearest Neighbor Queries in Shared-Nothing Environments, Geoinformatica, v.1 n.4, p.369-392, December 1997 [doi>10.1023/A:1009758427967]
• 19: Jignesh Patel , JieBing Yu , Navin Kabra , Kristin Tufte , Biswadeep Nag , Josef Burger , Nancy Hall , Karthikeyan Ramasamy , Roger Lueder , Curt Ellmann , Jim Kupsch , Shelly Guo , Johan Larson , David De Witt , Jeffrey Naughton, Building a scaleable geo-spatial DBMS: technology, implementation, and evaluation, Proceedings of the 1997 ACM SIGMOD international conference on Management of data, p.336-347, May 11-15, 1997, Tucson, Arizona, United States
• 20: Franco P. Preparata , Michael I. Shamos, Computational geometry: an introduction, Springer-Verlag New York, Inc., New York, NY, 1985
• 21: Nick Roussopoulos , Stephen Kelley , Frédéric Vincent, Nearest neighbor queries, Proceedings of the 1995 ACM SIGMOD international conference on Management of data, p.71-79, May 22-25, 1995, San Jose, California, United States
• 22: Michael Stonebraker , Jim Frew , Kenn Gardels , Jeff Meredith, The SEQUOIA 2000 storage benchmark, Proceedings of the 1993 ACM SIGMOD international conference on Management of data, p.2-11, May 25-28, 1993, Washington, D.C., United States
• 23: Yannis Theodoridis , Emmanuel Stefanakis , Timos K. Sellis, Cost Models for Join Queries in Spatial Databases, Proceedings of the Fourteenth International Conference on Data Engineering, p.476-483, February 23-27, 1998

INDEX TERMS

Primary Classification:
  H. Information Systems
  H.2 DATABASE MANAGEMENT
      H.2.3 Languages
          Subjects: Query languages

Additional Classification:
  H. Information Systems
  H.2 DATABASE MANAGEMENT
      H.2.8 Database applications
          Subjects: Spatial databases and GIS

General Terms:
Algorithms, Design, Experimentation, Languages