Geo-relational algebra: A model and query language for geometric database systems

  • Ralf Hartmut Güting
Special Data
Part of the Lecture Notes in Computer Science book series (LNCS, volume 303)


The user's conceptual model of a database system for geometric data should be simple and precise: easy to learn and understand, with clearly defined semantics, expressive: allow to express with ease all desired query and data manipulation tasks, efficiently implementable.

To achieve these goals we propose to extend relational database management systems by integrating geometry at all levels: At the conceptual level, relational algebra is extended to include geometric data types and operators. At the implementation level, the wealth of algorithms and data structures for geometric problems developed in the past decade in the field of Computational Geometry is exploited. — The paper starts from a view of relational algebra as a many-sorted algebra which allows to easily embed geometric data types and operators. A concrete algebra for two-dimensional applications is developed. It can be used as a highly expressive retrieval and data manipulation language for geometric as well as standard data. Finally, geo-relational database systems and their implementation strategy are discussed.


Database System Geometric Object Query Language Relational Algebra Geometric Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BeO79]
    Bentley, J.L., and Th. Ottmann, Algorithms for Reporting and Counting Geometric Intersections. IEEE Transactions on Computers C-28 (1979), 643–647.Google Scholar
  2. [BeS77]
    Berman, R.R., and M. Stonebraker, GEO-QUEL: A System for the Manipulation and Display of Geographic Data. Computer Graphics 11 (1977), 186–191.Google Scholar
  3. [Bu84]
    Buchmann, A.P., Current Trends in CAD Databases. Computer-Aided Design 16 (1984), 123–126.Google Scholar
  4. [ChF80]
    Chang, N.S., and K.S. Fu, A Relational Database System for Images. In: S.K. Chang and K.S. Fu (eds.), Pictorial Information Systems, Springer, 1980, 288–321.Google Scholar
  5. [ChF81]
    Chang, N.S., and K.S. Fu, Picture Query Languages for Pictorial Data-Base Systems. Computer 11 (1981), 23–33.Google Scholar
  6. [ChCK81]
    Chock, M., A.F. Cardenas, and A. Klinger, Manipulating Data Structures in Pictorial Information Systems. Computer 11 (November 1981), 43–50.Google Scholar
  7. [Da86]
    Date, C.J., An Introduction to Database Systems. Addison-Wesley, 1986.Google Scholar
  8. [Day86]
    Dayal, U., and J.M. Smith, PROBE: A Knowledge-Oriented Database Management System. In: M.L. Brodie and J. Mylopoulos (eds.), On Knowledge Base Management Systems: Integrating Artificial Intelligence and Database Technologies, Springer, 1986, 227–257.Google Scholar
  9. [Fr81]
    Frank, A., Application of DBMS to Land Information Systems. Proc. of the 7th VLDB Conf., Cannes, 1981, 448–453.Google Scholar
  10. [GoTW78]
    Goguen, J.A., J.W. Thatcher, and E.G. Wagner, An Initial Algebra Approach to the Specification, Correctness, and Implementation of Abstract Data Types. In: R. Yeh (ed.), Current Trends in Programming Methodology, Vol. IV, Prentice Hall 1978, 80–149.Google Scholar
  11. [Gr72]
    Graham, R.L., An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set. Information Processing Letters 1 (1972), 132–133.Google Scholar
  12. [Gü87]
    Güting, R.H., Modelling Non-Standard Database Systems by Many-Sorted Algebras. Fachbereich Informatik, Universität Dortmund, manuscript in preparation, 1987.Google Scholar
  13. [GüS87]
    Güting, R.H., and W. Schilling, A Practical Divide-and-Conquer Algorithm for the Rectangle Intersection Problem. Information Sciences 42 (1987), 95–112.Google Scholar
  14. [GüZC87]
    Güting, R.H., R. Zicari, and D. Choy, An Algebra for Structured Office Documents. IBM Almaden Research Center, San Jose, California, Report RJ 5559, 1987.Google Scholar
  15. [Gu84]
    Guttman, A., R-Trees: A Dynamic Index Structure for Spatial Searching. Proc. of the ACM SIGMOD Conf. on Management of Data, Boston, 1984, 47–57.Google Scholar
  16. [Ki83]
    Kirkpatrick, D., Optimal Search in Planar Subdivisions. SIAM Journal of Computing 12 (1983), 28–35.CrossRefGoogle Scholar
  17. [LiN87]
    Lipeck, U., and K. Neumann, Modelling and Manipulating Objects in Geoscientific Databases. In: S. Spaccapietra (ed.), Proc. of the 5th Int. Conf. on the Entity-Relationship Approach, Dijon, 1986, North-Holland, 1987, 67–86.Google Scholar
  18. [MaC80]
    Mantey, P.E., and E.D. Carlson, Integrated Geographic Data Bases: The GADS Experience. In: A. Blaser (ed.), Data Base Techniques for Pictorial Applications, Springer, 1980, 173–198.Google Scholar
  19. [Me84]
    Mehlhorn, K., Data Structures and Algorithms 3: Multi-dimensional Searching and Computational Geometry. Springer, 1984.Google Scholar
  20. [NaW79]
    Nagy, G., and S. Wagle, Geographic Data Processing. Computing Surveys 11 (1979), 139–181.Google Scholar
  21. [NiHS84]
    Nievergelt, J., H. Hinterberger, and K.C. Sevcik, The Grid File: An Adaptable, Symmetric Multikey File Structure. ACM Transactions on Database Systems 9 (1984), 38–71.CrossRefGoogle Scholar
  22. [NiP82]
    Nievergelt, J., and F.P. Preparata, Plane-Sweep Algorithms for Intersecting Geometric Figures. Communications of the ACM 25 (1982), 739–747.Google Scholar
  23. [Or86]
    Orenstein, J.A., Spatial Query Processing in an Object-Oriented Database System. Proc. of the ACM SIGMOD Conf. 1986, 326–336.Google Scholar
  24. [OtW86]
    Ottmann, Th., and D. Wood, Space-Economical Plane-Sweep Algorithms. Computer Vision, Graphics, and Image Processing 34 (1986), 35–51.Google Scholar
  25. [PrS85]
    Preparata, F.P., and M.I. Shamos, Computational Geometry: An Introduction. Springer 1985.Google Scholar
  26. [SaT86]
    Sarnak, N., and R.E. Tarjan, Planar Point Location Using Persistent Search Trees. Communications of the ACM 29 (1986), 669–679.CrossRefGoogle Scholar
  27. [ScWa86]
    Schek, H.J., and W. Waterfeld, A Database Kernel System for Geoscientific Applications. Proc. of the 2nd Int. Symp. on Spatial Data Handling, Seattle, WA, 1986, 273–288.Google Scholar
  28. [ScWe86]
    Schek, H.J., and G. Weikum, DASDBS: Concepts and Architecture of a Database System for Advanced Applications. TU Darmstadt, West Germany, Report DVSI-1986-T1, 1986.Google Scholar
  29. [ShH75]
    Shamos, M.I., and D. Hoey, Closest-Point Problems. Proc. of the 16th Annual IEEE Symposium on Foundations of Computer Science, 1975, 151–162.Google Scholar
  30. [StRG83]
    Stonebraker, M., B. Rubenstein, and A. Guttmann, Application of Abstract Data Types and Abstract Indices to CAD Data Bases. Proc. of the ACM/IEEE Conf. on Engineering Design Applications, San Jose, 1983, 107–113.Google Scholar
  31. [SzVW83]
    Szymansky, T.G., and C.J. van Wyk, Space Efficient Algorithms for VLSI Artwork Analysis. Proc. of the 20th IEEE Design Automation Conference, 1983, 734–739.Google Scholar
  32. [Ta82]
    Tamminen, M., Efficient Spatial Access to a Data Base. Proc. of the ACM SIGMOD Conf. 1982, 200–206.Google Scholar
  33. [TiMT83]
    Tikkanen, M., M. Mantyla, and M. Tamminen, GWB/DMS: A Geometric Data Manager. Proc. of the Eurographics Conf., Zagreb, 1983, 99–111.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Ralf Hartmut Güting
    • 1
  1. 1.Fachbereich InformatikUniversität DortmundDortmund 50West Germany

Personalised recommendations