Hashing by proximity to process duplicates in spatial databases

ABSTRACT

In a spatial database, an object may extend arbitrarily in space. As a result, many spatial data structures (e.g., the quadtree, the cell tree, the R+-tree) represent an object by partitioning it into multiple, yet simple, pieces, each of which is stored separately inside the data structure. Many operations on these data structures are likely to produce duplicate results because of the multiplicity of object pieces. A novel approach for duplicate processing based on proximity of spatial objects is presented. This is different from conventional duplicate elimination in database systems because, with spatial databases, different pieces of the same object can span multiple buckets of the underlying data structure. Example algorithms are presented to perform duplicate processing using proximity for quadtree representation of line segments and arbitrary rectangles. The complexity of the algorithms is seen to depend on a geometric classification of different instances of the spatial objects. By using proximity and the spatial properties of the objects, the number of disk-I/O requests as well as the run-time storage during duplicate processing can be reduced.

REFERENCES

• 1: Walid G. Aref , Hanan Samet, Efficient processing of window queries in the pyramid data structure, Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems, p.265-272, April 02-04, 1990, Nashville, Tennessee, United States [doi>10.1145/298514.298579]
• 2: W. G. Aref and H. Samet. Uniquely reporting spatial objects: Yet another operation for comparing spatial data structures. In Proceedings o.f the 5th International Symposium on Spatial Data Handling, pages 178-189, Charleston, SC, August 1992.
• 3: M. B. Dillencourt and H. Samet. Using topological sweep to extract the boundaries of regions in maps represented by region quadtrees. Submitted for publication, 1991.
• 4: Michael B. Dillencourt , Hannan Samet , Markku Tamminen, A general approach to connected-component labeling for arbitrary image representations, Journal of the ACM (JACM), v.39 n.2, p.253-280, April 1992 [doi>10.1145/128749.128750]
• 5: Ramez Elmasri , Shamkant B. Navathe, Fundamentals of database systems, Benjamin-Cummings Publishing Co., Inc., Redwood City, CA, 1989
• 6: Christos Faloutsos , Timos Sellis , Nick Roussopoulos, Analysis of object oriented spatial access methods, Proceedings of the 1987 ACM SIGMOD international conference on Management of data, p.426-439, May 27-29, 1987, San Francisco, California, United States
• 7: Michael J. Folk, File Structures, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1999
• 8: Oliver Günther, The Design of the Cell Tree: An Object-Oriented Index Structure for Geometric Databases, Proceedings of the Fifth International Conference on Data Engineering, p.598-605, February 06-10, 1989
• 9: 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
• 10: A Klinger. Patterns and search statistics. In J. S. Rustagi, editor, Optimizing Methods in Statistics, pages 303-337. Academic Press, New York, 1971.
• 11: Randal C. Nelson , Hanan Samet, A consistent hierarchical representation for vector data, ACM SIGGRAPH Computer Graphics, v.20 n.4, p.197-206, Aug. 1986
• 12: J. Nievergelt , Hans Hinterberger , Kenneth C. Sevcik, The Grid File: An Adaptable, Symmetric Multikey File Structure, ACM Transactions on Database Systems (TODS), v.9 n.1, p.38-71, March 1984 [doi>10.1145/348.318586]
• 13: Azriel Rosenfeld , Avinash C. Kak, Digital Picture Processing, Academic Press, Inc., Orlando, FL, 1982
• 14: Hanan Samet, Connected Component Labeling Using Quadtrees, Journal of the ACM (JACM), v.28 n.3, p.487-501, July 1981 [doi>10.1145/322261.322267]
• 15: Hanan Samet, Applications of spatial data structures: Computer graphics, image processing, and GIS, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1990
• 16: Hanan Samet, The design and analysis of spatial data structures, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1990

INDEX TERMS

Primary Classification:
  E. Data
  E.2 DATA STORAGE REPRESENTATIONS
      Subjects: Hash-table representations

Additional Classification:
  H. Information Systems
  H.2 DATABASE MANAGEMENT

General Terms:
Theory