Abstract
In this paper we discuss two data models for spatial database systems: the linear data model and the topological data model. Both can be used to model a wide range of applications. The linear data model is particularly suited to model spatial database applications in which exact geometrical information is required and in which this information can be approximated by linear geometrical spatial objects. The topological model on the other hand is suitable for applications in which rather than exact geometrical information the relative position of spatial objects is of importance.
We will specify in each case which types of spatial data and spatial databases are under consideration. A semantics for both data models is formally defined in terms of finite representations of spatial databases in the data models. We also present languages to query spatial databases in both models and briefly investigate their expressiveness.
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S. Abiteboul, R. Hull, and V. Vianu, Foundations of Databases, Addison-Wesley Publishing Company, 1995.
F. Afrati, S. Cosmadakis, S. Grumbach, and G. Kuper, “Linear Versus Polynomial Constraints in Database Query Languages,” in Proceedings 2nd Int'l Workshop on Principles and Practice of Constraint Programming (Rosario, WA), A. Borning, ed., Lecture Notes in Computer Science, vol. 874, Springer-Verlag, Berlin, 1994, 181–192.
A. Brodsky, J. Jaffar, and M.J. Maher, “Toward Practical Constraint Databases,” in Proceedings 19th Int'l Conf. on Very Large Databases (Dublin, Ireland), 1993, 567–580.
A. Brodsky and Y. Kornatzky, “The LyriC Language: Querying Constraint Objects,” in Proceedings Post-ILPS'94 Workshop on Constraints and Databases (Ithaca, NY), 1994.
A. Brøndsted, An Introduction to Convex Polytopes, Graduate Texts in Mathematics, vol. 90, Springer-Verlag, New York, 1983.
I. Carlbom, “An Algorithm for Geometric Set Operations Using Cellular Subdivision Techniques,” IEEE Computer Graphics and Applications, 7:5, 1987, 44–55.
A. Chandra and D. Harel, “Computable Queries for Relational Database Systems,” Journal of Computer and System Sciences, 21:2, 1980, 156–178.
J.P. Corbett. Topological Principles of Cartography. Technical Paper No. 48, US Bureau of the Census, Washington, DC, USA: US Government Printing Office, 1979.
M.J. Egenhofer, “A Formal Definition of Binary Topological Relationships,” in Proceedings Foundations of Data Organization and Algorithms, W. Litwin and H.-J. Schek, eds., Lecture Notes in Computer Science, vol. 367, Springer-Verlag, Berlin, 1989, 457–472.
J. Egenhofer, “Why not SQL!”, Int'l J. on Geographical Information Systems, 6:2, 1992, 71–85.
O. Günther, ed., Efficient Structures for Geometric Data Management, Lecture Notes in Computer Science, vol. 337, Springer-Verlag, Berlin, 1988.
O. Günther and A. Buchmann, Research Issues in Spatial Databases, in Sigmod Record, vol. 19, 4, 61–68, 1990.
R.H. Güting, “Geo-Relational Algebra: A Model and Query Language for Geometric Database Systems,” in Advances in Database Technology-EDBT '88, Proceedings Int'l Conf. on Extending Database Technology (Venice, Italy), J.W. Schmidt, S. Ceri, and M. Missikoff, eds., Lecture Notes in Computer Science, vol. 303, Springer-Verlag, Berlin, 1988, 506–527.
R.H. Güting, “Gral: An Extensible Relational Database System for Geometric Applications,” in Proceedings 15th Int'l Conf. on Very Large Databases (Amsterdam, the Netherlands), 1989, 33–34.
R.H. Güting, “An Introduction to Spatial Database Systems,” VLDB-Journal, 3:4, 1994, 357–399.
T. Huynh, C. Lassez, and J. L. Lassez.Fourier Algorithm Revisited. In Proceedings 2nd Int'l Conf, on Algebraic an Logic Programming, H. Kirchner and W. Wechler, eds. Lecture Notes in Computer Science, vol. 463. Springer Verlag, Berlin, 1990, 117–131.
P.J. Kelly and M.L. Weiss. Geometry and Convexity: a Study in Mathematical Methods, J. Wiley and Sons, New York, 1979.
P.C. Kanellakis, G.M. Kuper and P.Z. Revesz, “Constraint Query Languages,” Journal of Computer and System Sciences, to appear, also in Proceedings 9th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (Nashville, TN), 1990, 299–313.
B. Kuijpers, J. Paredaens, and J. Van den Bussche “Lossless representation of topological spatial data,” in Proceedings 4th Symposium on Advances in Spatial Databases, M. J. Egenhofer and J. R. Herring, eds., Lecture Notes in Computer Science, vol. 951. Springer Verlag, Berlin, 1995, 1–13.
J.-L. Lassez, “Querying Constraints,” in Proceedings 9th ACM SIGACTSIGMOD-SIGART Symposium on Principles of Database Systems (Nashville, TN), 1990, 288–298.
R. Laurini and D. Thompson. Fundamentals of Spatial Information Systems. The A.P.I.C. Series, 37, Academic Press, 1992.
M. Liebling and A. Prodon, “Algorithmic Geometry,” in Scientific Visualization and Graphics Simulation, D. Thalmann, ed., J. Wiley and Sons. 14–25.
P. McMullen and G.C. Shephard, Convex Polytopes and the Upper Bound Conjecture, University Press, Cambridge, 1971.
E.E. Moise. Geometric Topology in Dimensions 2 and 3. Graduate Texts in Mathematics, vol. 47, Springer-Verlag, 1977.
J. Paredaens, J. Van den Bussche, and D. Van Gucht, “Towards a Theory of Spatial Database Queries,” in Proceedings 13th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (Minneapolis, MN), 1994. 279–288.
J. Paredaens. Spatial Databases. The Final Frontier. Database Theory-ICDT '95, Lecture Notes in Computer Science, vol. 893, 14–32, Springer-Verlag, 1995.
F.P. Preparata and D.E. Muller. “Finding the Intersection of n Half-Spaces in Time O(nlogn),” Theoretical Computer Science, 8, 1979, 45–55.
L.K. Putnam and P.A. Subrahmanyam, “Boolean Operations on n-Dimensional Objects,” IEEE Computer Graphics and Applications, 6:6, 1986, 43–51.
N. Roussopoulos, C. Faloutsos, and T. Sellis, “An Efficient Pictorial Database System for PSQL,” IEEE Transactions on Software Engineering, 14:5, 1988, 639–650.
W. Schwabhauser, W. Szmielew, and A. Tarski. Metamathematische Methoden in der Geometrie, Springer-Verlag, Berlin, 1983.
P. Svensson and Z. Huang, “Geo-Sal: A Query Language for Spatial Data Analysis,” in Proceedings 2nd Symposium on Advances in Spatial Databases, O. Günther and H.-J. Schek, eds. Lecture Notes in Computer Science, vol. 525. Springer-Verlag, Berlin,1991, 119–140.
B. Tilove, “Set Membership Classification: a Unified Approach to Geometric Intersection Problems,” IEEE Transactions on Computers, C-29:10, 1980, 874–883.
L. Vandeurzen, M. Gyssens, and D. Van Gucht, “On the Desirability and Limitations of Linear Spatial Query Languages,” in Proceedings 4th Symposium on Advances in Spatial Databases, M. J. Egenhofer and J. R. Herring, eds., Lecture Notes in Computer Science, vol. 951. Springer Verlag, Berlin, 1995, 14–28.
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Kuijpers, B., Paredaens, J., Vandeurzen, L. (1998). Semantics in spatial databases. In: Thalheim, B., Libkin, L. (eds) Semantics in Databases. SiD 1995. Lecture Notes in Computer Science, vol 1358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035007
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DOI: https://doi.org/10.1007/BFb0035007
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