Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Database Programming Languages

DBPL 2001: Database Programming Languages pp 182–197Cite as

Linear Approximation of Semi-algebraic Spatial Databases Using Transitive Closure Logic, in Arbitrary Dimension

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2397))

Abstract

We consider n-dimensional semi-algebraic spatial databases. We compute in first-order logic extended with a transitive closure operator, a linear spatial database which characterizes the semi-algebraic spatial database up to a homeomorphism. In this way, we generalize our earlier results to semi-algebraic spatial databases in arbitrary dimensions, our earlier results being true for only two dimensions.

Consequently, we can prove that first-order logic with a transitive closure operator extended with stop conditions, can express all Boolean topological queries on semi-algebraic spatial databases of arbitrary dimension.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Benedetti and J.J. Risler. Real Algebraic and Semi-algebraic Sets. Hermann, Paris, 1990.

    MATH  Google Scholar 

  2. M. Benedikt, G. Dong, L. Libkin, and L. Wong. Relational expressive power of constraint query languages. Journal of the ACM, 45(1):1–34, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  3. M. Benedikt, M. Grohe, L. Libkin, and L. Segoufin. Reachability and connectivity queries in constraint databases. In Proceedings of the 19th ACM Symposium on Principles of Database Systems, pages 104–115. ACM Press, 2000.

    Google Scholar 

  4. M. Benedikt and L. Libkin. Safe constraint queries. SIAM Journal of Computing, 29(5):1652–1682, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Bochnak, M. Coste, and M.-F. Roy. Real Algebraic Geometry, volume 36 of Ergebenisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, 1998.

    Google Scholar 

  6. A. Chandra and D. Harel. Computable queries for relational data bases. Journal of Computer and System Sciences, 21(2):156–178, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  7. F. Geerts and B. Kuijpers. Expressing topological connectivity of spatial databases. In Research Issues in Structured and Semistructured Database Programming. Proceedings of the 8th International Workshop on Database Programming Languages, volume 1949 of Lecture Notes in Computer Science, pages 224–238. Springer-Verlag, 1999.

    Chapter  Google Scholar 

  8. F. Geerts and B. Kuijpers. Linear approximation of planar spatial databases using transitive-closure logic. In Proceedings of the 19th ACM Symposium on Principles of Database Systems, pages 126–135. ACM Press, 2000.

    Google Scholar 

  9. S. Grumbach and G. Kuper. Tractable recursion over geometric data. In G. Smolka, editor, Proceedings of the 3rd Conference on Principles and Practice of Constraint Programming, volume 1330 of Lecture Notes in Computer Science, pages 450–462. Springer-Verlag, 1997.

    Chapter  Google Scholar 

  10. S. Grumbach and J. Su. Finitely representable databases. Journal of Computer and System Sciences, 55(2):273–298, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  11. S. Grumbach and J. Su. Queries with arithmetical constraints. Theoretical Computer Science, 173(1):151–181, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  12. V. Guillemin and A. Pollack. Differential topology. Prentice-Hall, 1974.

    Google Scholar 

  13. M. Gyssens, J. Van den Bussche, and D. Van Gucht. Complete geometrical query languages. Journal of Computer and System Sciences, 58(1):483–511, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  14. P.C. Kanellakis, G.M. Kuper, and P.Z. Revesz. Constraint query languages. Journal of Computer and System Science, 51(1):26–52, 1995.

    Article  MathSciNet  Google Scholar 

  15. S. Kreutzer. Fixed-point query languages for linear constraint databases. In Proceedings of the 19th ACM Symposium on Principles of Database Systems, pages 116–125. ACM Press, 2000.

    Google Scholar 

  16. S. Kreutzer. Query languages for constraint databases: First-order logic, fixed-points, and convex hulls. In J. Van den Bussche and V. Vianu, editors, Proceedings of the 9th International Conference on Database Theory, volume 1973 of Lecture Notes in Computer Science, pages 248–262. Springer-Verlag, 2001.

    Google Scholar 

  17. G.M. Kuper, J. Paredaens, and L. Libkin, editors. Constraint Databases. Springer-Verlag, 1999.

    Google Scholar 

  18. E. Rannou. The complexity of stratification computation. Discrete and Computational Geometry, 19:47–79, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  19. M. Shiota. Geometry of Subanalytic and Semialgebraic Sets. Birkhäuser, 1997.

    Google Scholar 

  20. L. Vandeurzen, M. Gyssens, and D. Van Gucht. An expressive language for linear spatial database queries. In Proceedings of the 17th ACM Symposium on Principles of Database Systems, pages 109–118. ACM Press, 1998.

    Google Scholar 

  21. L. Vandeurzen, M. Gyssens, and D. Van Gucht. On query languages for linear queries definable with polynomial constraints. In E. F. Freuder, editor, Proceedings of the 2nd Conference on Principles and Practice of Constraint Programming, volume 1118 of Lecture Notes in Computer Science, pages 468–481, Springer-Verlag, 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Limburg, Belgium

    Floris Geerts

Authors
  1. Floris Geerts
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Univesità di Pisa, Corso Italia 40, 56125, Pisa, Italy

    Giorgio Ghelli

  2. Department of Computer Science, Concordia University, 1455 De Maisonneuve Blvd. West, Montréal, Québec, Canada, H3G 1M8

    Gösta Grahne

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Geerts, F. (2002). Linear Approximation of Semi-algebraic Spatial Databases Using Transitive Closure Logic, in Arbitrary Dimension. In: Ghelli, G., Grahne, G. (eds) Database Programming Languages. DBPL 2001. Lecture Notes in Computer Science, vol 2397. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46093-4_11

Download citation

  • DOI: https://doi.org/10.1007/3-540-46093-4_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44080-2

  • Online ISBN: 978-3-540-46093-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation