Abstract
The increasing popularity of web-based mapping services such as Microsoft Virtual Earth and Google Maps/Earth has led to a dramatic increase in awareness of the importance of location as a component of data for the purposes of further processing as a means of enhancing the value of the nonspatial data and of visualization. Both of these purposes inevitably involve searching. The efficiency of searching is dependent on the extent to which the underlying data is sorted. The sorting is encapsulated by the data structure known as an index that is used to represent the spatial data thereby making it more accessible. The traditional role of the indexes is to sort the data, which means that they order the data. However, since generally no ordering exists in dimensions greater than 1 without a transformation of the data to one dimension, the role of the sort process is one of differentiating between the data and what is usually done is to sort the spatial objects with respect to the space that they occupy. The resulting ordering should be implicit rather than explicit so that the data need not be resorted (i.e., the index need not be rebuilt) when the queries change. The indexes are said to order the space and the characteristics of such indexes are explored further.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Ang, C.-H., Samet, H., and Shaffer, C. A. (1990) A new region expansion for quadtrees, IEEE Transactions on Pattern Analysis and Machine Intelligence 12, 682–686, Also see Proceedings of the Third International Symposium on Spatial Data Handling, pp. 19–37, Sydney, Australia, August 1988.
Aref, W. G. and Samet, H. (1990) Efficient processing of window queries in the pyramid data structure, In Proceedings of the 9th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS), Nashville, TN, pp. 265–272, Also in Proceedings of the Fifth Brazilian Symposium on Databases, pp. 15–26, Rio de Janeiro, Brazil, April 1990.
Aref, W. G. and Samet, H. (1992) Uniquely reporting spatial objects: yet another operation for comparing spatial data structures, In Proceedings of the 5th International Symposium on Spatial Data Handling, Charleston, SC, pp. 178–189.
Aref, W. G. and Samet, H. (1994) Hashing by proximity to process duplicates in spatial databases, In Proceedings of the 3rd International Conference on Information and Knowledge Management (CIKM), Gaithersburg, MD, pp. 347–354.
Arnold, K. and Gosling, J. (1996) The JAVA— Programming Language, Reading, MA, Addison-Wesley.
Ayala, D., Brunet, P., Juan, R., and Navazo, I. (1985) Object representation by means of nonminimal division quadtrees and octrees, ACM Transactions on Graphics 4, 41–59.
Beckmann, N., Kriegel, H.-P., Schneider, R., and Seeger, B. (1990) The R,-tree: an efficient and robust access method for points and rectangles, In Proceedings of the ACM SIGMOD Conference, Atlantic City, NJ, pp. 322–331.
Brabec, F. and Samet, H. (1998a) The VASCO R-tree JAVA—Applet, In Y. Ioannidis and W. Klas (eds.), Visual Database Systems (VDB4). Proceedings of the IFIP TC2/WG2.6 Fourth Working Conference on Visual Database Systems, L'Aquila, Italy, pp. 123–140, Chapman and Hall.
Brabec, F. and Samet, H. (1998b) Visualizing and animating R-trees and spatial operations in spatial databases on the worldwide web, In Y. Ioannidis and W. Klas (eds.), Visual Database Systems (VDB4). Proceedings of the IFIP TC2//WG2.6 Fourth Working Conference on Visual Database Systems, L'Aquila, Italy, pp. 147–153, Chapman and Hall.
Brabec, F. and Samet, H. (2000) Visualizing and animating search operations on quadtrees on the worldwide web, In K. Kedem and M. Katz (eds.), Proceedings of the 16th European Workshop on Computational Geometry, Eilat, Israel, pp. 70–76.
Brabec, F. and Samet, H. (2007) Client-based spatial browsing on the world wide web, IEEE Internet Computing 11, 52–59.
Brabec, F., Samet, H., and Yilmaz, C. (2003) VASCO: visualizing and animating spatial constructs and operations, In Proceedings of the 19th Annual Symposium on Computational Geometry, San Diego, CA, pp. 374–375.
Brabec, F., Samet, H., and Yilmaz, C. (2003) VASCO: visualizing and animating spatial constructs and operations, In Proceedings of the 19th Annual Symposium on Computational Geometry, San Diego, CA, pp. 374–375.
Dittrich, J.-P. and Seeger, B. (2000) Data redundancy and duplicate detection in spatial join processing, In Proceedings of the 16th IEEE International Conference on Data Engineering, San Diego, CA, pp. 535–546.
Dyer, C. R. (1980) Computing the Euler number of an image from its quadtree, Computer Graphics and Image Processing 13, 270–276, Also University of Maryland Computer Science Technical Report TR—769, May 1979.
Dyer, C. R., Rosenfeld, A., and Samet, H. (1980) Region representation: boundary codes from quadtrees, Communications of the ACM 23, 171–179, Also University of Maryland Computer Science Technical Report TR—732, February 1979.
Esperança, C. and Samet, H. (2002) Experience with SAND/Tcl: a scripting tool for spatial databases, Journal of Visual Languages and Computing 13, 229–255.
Fuchs, H., Abram, G. D., and Grant, E. D. (1983) Near real-time shaded display of rigid objects, Computer Graphics 17, 65–72, Also in Proceedings of the SIGGRAPH'83 Conference, Boston, July 1983.
Fuchs, H., Kedem, Z. M., and Naylor, B. F. (1980) On visible surface generation by a priori tree structures, Computer Graphics 14, 124–133, Also in Proceedings of the SIGGRAPH'80 Conference, Seattle, WA, July 1980.
Glassner, A. S. (1984) Space subdivision for fast ray tracing, IEEE Computer Graphics and Applications 4, 15–22.
Guttman, A. (1984) R-trees: a dynamic index structure for spatial searching, In Proceedings of the ACM SIGMOD Conference, Boston, pp. 47–57.
Hoel, E. G. and Samet, H. (1991) Efficient processing of spatial queries in line segment databases, In O. Günther and H.-J. Schek (eds.), Advances in Spatial Databases — 2nd Symposium, SSD'91, Zurich, Switzerland, pp. 237–256.
Hoel, E. G. and Samet, H. (1995) Benchmarking spatial join operations with spatial output, In U. Dayal, P. M. D. Gray, and S. Nishio (eds.), Proceedings of the 21st International Conference on Very Large Data Bases (VLDB), Zurich, Switzerland, pp. 606–618.
Hunter, G. M. (1978) Efficient computation and data structures for graphics, PhD thesis, Department of Electrical Engineering and Computer Science, Princeton University, Princeton, NJ.
Hunter, G. M. and Steiglitz, K. (1979) Operations on images using quad trees, IEEE Transactions on Pattern Analysis and Machine Intelligence 1, 145–153.
Jacox, E. and Samet, H. (2007) Spatial join techniques, ACM Transactions on Database Systems 32, 7. Also an expanded version in University of Maryland Computer Science Technical Report TR— 4730, June 2005.
Kim, Y. J. and Patel, J. M. (2007) Rethinking choices for multi-dimensional point indexing: making the case for the often ignored quadtree, In Proceedings of the Third Biennial Conference on Innovative Data Systems Research (CIDR 2007), Asilomar, CA, pp. 281– 291.
Klinger, A. (1971) Patterns and search statistics, In J. S. Rustagi (ed.), Optimizing Methods in Statistics, New York, Academic Press, pp. 303–337.
Knuth, D. E. (1998) The Art of Computer Programming: Sorting and Searching, Vol. 3, Reading, MA, Addison-Wesley, Second edition.
Marchionini, G., Samet, H., and Brandt, L. (2003) Introduction to the digital government special issue, Communications of the ACM 46, 24–27.
Meagher, D. (1982) Geometric modelling using octree encoding, Computer Graphics and Image Processing 19, 129–147.
Nelson, R. C. and Samet, H. (1986) A consistent hierarchical representation for vector data, Computer Graphics 20, 197–206. Also in Proceedings of the SIGGRAPH'86 Conference, Dallas, TX, August 1986.
Nelson, R. C. and Samet, H. (1987) A population analysis for hierarchical data structures. In Proceedings of the ACM SIGMOD Conference, San Francisco, pp. 270–277.
Orenstein, J. A. (1982) Multidimensional tries used for associative searching, Information Processing Letters 14, 150–157.
Preparata, F. P. and Shamos, M. I. (1985) Computational geometry: an introduction, New York, Springer.
Robinson, J. T. (1981) The K-D-B-tree: a search structure for large multidimensional dynamic indexes, In Proceedings of the ACM SIGMOD Conference, Ann Arbor, MI, pp. 10–18.
Sagan, H. (1994) Space-Filling Curves, New York, Springer.
Samet, H. (1980a) Region representation: quadtrees from binary arrays, Computer Graphics and Image Processing 13, 88–93. Also University of Maryland Computer Science Technical Report TR—767, May 1979.
Samet, H. (1980b) Region representation: quadtrees from boundary codes, Communications of the ACM 23, 163–170. Also University of Maryland Computer Science Technical Report TR—741, March 1979.
Samet, H. (1981a) An algorithm for converting rasters to quadtrees, IEEE Transactions on Pattern Analysis and Machine Intelligence 3, 93–95. Also University of Maryland Computer Science Technical Report TR—766, May 1979.
Samet, H. (1981b) Computing perimeters of images represented by quadtrees, IEEE Transactions on Pattern Analysis and Machine Intelligence 3, 683–687. Also University of Maryland Computer Science Technical Report TR—755, April 1979.
Samet, H. (1981c) Connected component labeling using quadtrees, Journal of the ACM 28, 487–501. Also University of Maryland Computer Science Technical Report TR—756, April 1979.
Samet, H. (1982) Distance transform for images represented by quadtrees, IEEE Transactions on Pattern Analysis and Machine Intelligence 4, 298–303. Also University of Maryland Computer Science Technical Report TR—780, July 1979.
Samet, H. (1983) A quadtree medial axis transform, Communications of the ACM 26, 680–693. Also see CORRIGENDUM, Communications of the ACM 27(2), 151, February 1984 and University of Maryland Computer Science Technical Report TR—803, August 1979.
Samet, H. (1984) Algorithms for the conversion of quadtrees to rasters, Computer Vision, Graphics, and Image Processing 26, 1–16. Also University of Maryland Computer Science Technical Report TR—979, November 1980.
Samet, H. (1985) Reconstruction of quadtrees from quadtree medial axis transforms, Computer Vision, Graphics, and Image Processing 29, 311–328. Also University of Maryland Computer Science Technical Report TR—1224, October 1982.
Samet, H. (1988) An overview of quadtrees, octrees, and related hierarchical data structures, In R. A. Earnshaw (ed.), Theoretical Foundations of Computer Graphics and CAD, Vol. 40 of NATO ASI Series F: Computer and System Sciences, Berlin, West Germany, Springer, pp. 51–68.
Samet, H. (1989a) Implementing ray tracing with octrees and neighbor finding, Computers & Graphics 13, 445–460. Also University of Maryland Computer Science Technical Report TR—2204, February 1989.
Samet, H. (1989b) Neighbor finding in images represented by octrees, Computer Vision, Graphics, and Image Processing 46, 367–386. Also University of Maryland Computer Science Technical Report TR—1968, January 1988.
Samet, H. (1990a) Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS, Reading, MA, Addison-Wesley.
Samet, H. (1990b) The Design and Analysis of Spatial Data Structures, Reading, MA, Addison-Wesley.
Samet, H. (2004) Decoupling partitioning and grouping: overcoming shortcomings of spatial indexing with bucketing, ACM Transactions on Database Systems 29, 789–830. Also University of Maryland Computer Science Technical Report TR—4523, August 2003.
Samet, H. (2006) Foundations of Multidimensional and Metric Data Structures, San Francisco, Morgan-Kaufmann.
Samet, H., Alborzi, H., Brabec, F., Esperança, C., Hjaltason, G. R., Morgan, F., and Tanin, E. (2003) Use of the SAND spatial browser for digital government applications, Communications of the ACM 46, 63–66.
Samet, H., Sankaranarayanan, J., and Alborzi, H. (2008) Scalable network distance browsing in spatial databases, In Proceedings of the ACM SIGMOD Conference, Vancouver, Canada, pp. 43–54. Also University of Maryland Computer Science Technical Report TR—4865, April 2007 (SIGMOD 2008 Best Paper Award).
Samet, H. and Tamminen, M. (1985) Bintrees, CSG trees, and time, Computer Graphics 19, 121–130. Also In Proceedings of the SIGGRAPH'85 Conference, San Francisco, July 1985.
Samet, H. and Webber, R. E. (1985) Storing a collection of polygons using quadtrees, ACM Transactions on Graphics 4, 182–222. Also see Proceedings of Computer Vision and Pattern Recognition'83, pp. 127–132, Washington, DC, June 1983 and University of Maryland Computer Science Technical Report TR—1372, February 1984.
Sankaranarayanan, J., Alborzi, H., and Samet, H. (2005) Efficient query processing on spatial networks. In Proceedings of the 13th ACM International Symposium on Advances in Geographic Information Systems, Bremen, Germany, pp. 200–209.
Sellis, T., Roussopoulos, N., and Faloutsos, C. (1987) The R + -tree: a dynamic index for multi-dimensional objects, In P. M. Stocker and W. Kent (eds.), Proceedings of the 13th International Conference on Very Large Databases (VLDB), Brighton, United Kingdom, pp. 71–79. Also University of Maryland Computer Science Technical Report TR—1795, 1987.
Shaffer, C. A. and Samet, H. (1987) Optimal quadtree construction algorithms, Computer Vision, Graphics, and Image Processing 37, 402–419.
Shaffer, C. A., Samet, H., and Nelson, R. C. (1990) QUILT: a geographic information system based on quadtrees, International Journal of Geographical Information Systems 4, 103– 131. Also University of Maryland Computer Science Technical Report TR— 1885.1, July 1987.
Sivan, R. and Samet, H. (1992) Algorithms for constructing quadtree surface maps. In Proceedings of the 5th International Symposium on Spatial Data Handling, Vol. 1, Charleston, SC, pp. 361–370.
Tamminen, M. and Samet, H. (1984) Efficient octree conversion by connectivity labeling, Computer Graphics 18, 43–51. Also in Proceedings of the SIGGRAPH'84 Conference, Minneapolis, MN, July 1984.
Tanimoto, S. L. and Pavlidis, T. (1975) A hierarchical data structure for picture processing, Computer Graphics and Image Processing 4, 104–119.
Wang, W., Yang, J., and Muntz, R. (1998) PK-tree: a spatial index structure for high dimensional point data. In K. Tanaka and S. Ghandeharizadeh (eds.), Proceedings of the 5th International Conference on Foundations of Data Organization and Algorithms (FODO), Kobe, Japan, pp. 27–36. Also University of California at Los Angeles Computer Science Technical Report 980032, September 1998.
Warnock, J. E. (1968) A hidden line algorithm for halftone picture representation, Computer Science Technical Report TR 4–5, University of Utah, Salt Lake City, UT.
Warnock, J. E. (1969) A hidden surface algorithm for computer generated half tone pictures, Computer Science Technical Report TR 4–15, University of Utah, Salt Lake City, UT.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science + Business Media B.V.
About this paper
Cite this paper
Samet, H. (2009). Sorting Spatial Data by Spatial Occupancy. In: Amicis, R.D., Stojanovic, R., Conti, G. (eds) GeoSpatial Visual Analytics. NATO Science for Peace and Security Series C: Environmental Security. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2899-0_3
Download citation
DOI: https://doi.org/10.1007/978-90-481-2899-0_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-2898-3
Online ISBN: 978-90-481-2899-0
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)