Abstract
Although maps and partitions are ubiquitous in geographical information systems and spatial databases, there is only little work investigating their foundations. We give a rigorous definition for spatial partitions and propose partitions as a generic spatial data type that can be used to model arbitrary maps and to support spatial analysis. We identify a set of three powerful operations on partitions and show that the type of partitions is closed under them. These basic operators are sufficient to express all known application-specific operations. Moreover, many map operations will be considerably generalized in our framework. We also indicate that partitions can be effectively used as a meta-model to describe other spatial data types.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
J.K. Berry. Fundamental Operations in Computer-Assisted Map Analysis. Int. Journal of Geographical Information Systems, vol. 1, no. 2, pp. 119–136, 1987.
EYF. Chan & R. Zhu. QL/G: A Query Language for Geometric Databases. 1st Int. Conf on GIS in Urban and Environmental Planning, pp. 271–286, 1996.
J. Dangermond. A Classification of Software Components Commonly Used in Geographic Information Systems. Introductory Readings in Geographic Information Systems, Taylor & Francis, pp. 30–51, 1990.
J. Dugundji. Topology. Allyn and Bacon, Boston, 1966.
M.J. Egenhofer & R.D. Franzosa. Point-Set Topological Spatial Relations. Int. Journal of Geographical Information Systems, vol. 5, no. 2, pp. 161–174, 1991.
M.J. Egenhofer. Spatial SQL: A Spatial Query Language. Report 103, Dept. of Surveying Engineering, University of Maine, 1989.
M. Erwig & R.H. Güting. Explicit Graphs in a Functional Model for Spatial Databases. IEEE Transactions on Knowledge and Data Engineering, vol. 6, no. 5, pp. 787–804, 1994.
M. Erwig. Graphs in Spatial Databases. Doctoral Thesis, FernUniversitÄt Hagen, 1994.
M. Erwig. Functional Programming with Graphs. 2nd ACM SIGPLAN Int. Conf on Functional Programming, pp. 52–65, 1997.
M. Erwig & M. Schneider. Vague Regions. 5th Int. Symp. on Spatial Databases (SSD'97), 1997. To appear.
A.U. Frank. Overlay Processing in Spatial Information Systems. Proc. of the 8th Int. Symp. on Computer-Assisted Cartography, AUTOCARTO 8, pp. 16–31, 1987.
A.U. Frank. Spatial Concepts, Geometric Data Models and Data Structures. Computer and Geosciences, 1990.
A.U. Frank, G.S. Volta & M. MacGranaghan. Formalization of Families of Categorical Coverages. Int. Journal of Geographical Information Science, vol. 11, no. 3, pp. 215–231, 1997.
R.H. Güting & M. Schneider. Realm-Based Spatial Data Types: The ROSE Algebra. VLDB Journal, vol. 4, pp. 100–143, 1995.
R.H. Güting. Geo-Relational Algebra: A Model and Query Language for Geometric Database Systems. Int. Conf. on Extending Database Technology, LNCS 303, pp. 506–527, 1988.
Z. Huang, P Svensson & H. Hauska. Solving Spatial Analysis Problems with GeoSAL, A Spatial Query Language. 6th Int. Working Conf. on Scientific and Statistical Database Management, 1992.
H.-P. Kriegel, T. Brinkhoff & R. Schneider. The Combination of Spatial Access Methods and Computational Geometry in Geographic Database Systems. 2nd Symp. on Advances in Spatial Databases (SSD'91), LNCS 525, pp. 5–21, 1991.
U. Lipeck & K. Neumann. Modelling and Manipulating Objects in Geoscientific Databases. 5th Int. Conf. on the Entity-Relationship Approach, pp. 67–86, 1987.
PE. Mantey & E.D. Carlson. Integrated Geographic Data Bases: The GADS Experience. Data Base Techniques for Pictorial Applications, Springer, pp. 173–190, 1980.
G. Nagy & S. Wagle. Geographic Data Processing. ACM Computing Surveys, vol. 11, no. 2, pp. 139–181, 1979.
M. Schneider. Spatial Data Types for Database Systems. Doctoral Thesis, FernUniversität Hagen, 1995.
M. Scholl & A. Voisard. Thematic Map Modeling. 1st Int. Symp. on Large Spatial Databases (SSD'89), pp. 167–190,1989.
R.B. Tilove. Set Membership Classification: A Unified Approach to Geometric Intersection Problems. IEEE Transactions on Computers, vol. C-29, pp. 874–883, 1980.
C.D. Tomlin. Geographic Information Systems and Cartographic Modeling. Prentice Hall, 1990.
C.R. Valenzuela. Data Analysis and Modeling. Remote Sensing and Geographical Information Systems for Resource Management in Developing Countries, pp. 335–348, 1991.
G.S. Volta & M.J. Egenhofer. Interaction with Attribute Data Based on Categorical Coverages. Conf. on Spatial Information Theory (COSIT'93), LNCS 716, pp. 215–233, 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Erwig, M., Schneider, M. (1997). Partition and conquer. In: Hirtle, S.C., Frank, A.U. (eds) Spatial Information Theory A Theoretical Basis for GIS. COSIT 1997. Lecture Notes in Computer Science, vol 1329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63623-4_63
Download citation
DOI: https://doi.org/10.1007/3-540-63623-4_63
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63623-6
Online ISBN: 978-3-540-69616-2
eBook Packages: Springer Book Archive