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Region-Based Query Languages for Spatial Databases in the Topological Data Model

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Advances in Spatial and Temporal Databases (SSTD 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2750))

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Abstract

We consider spatial databases in the topological data model, i.e., databases that consist of a finite number of labeled regions in the real plane. Such databases partition the plane further into elementary regions. We propose a first-order language, which uses elementary-region variables and label variables, to query spatial databases. All queries expressible in this first-order logic are topological\/ and they can be evaluated in polynomial time. Furthermore, the proposed language is powerful enough to distinguish between any two spatial databases that are not topologically equivalent. This language does not allow the expression of all computable topological queries, however, as is illustrated by the connectivity query. We also study some more powerful extensions of this first-order language, e.g., with a while-loop. In particular, we describe an extension that is sound and computationally complete for the topological queries on spatial databases in the topological data model.

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References

  1. Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)

    MATH  Google Scholar 

  2. Benedikt, M., Grohe, M., Libkin, L., Segoufin, L.: Reachability and connectivity queries in constraint databases. In: Proceedings of the 19th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS 2000), pp. 104–115 (2000)

    Google Scholar 

  3. Bochnak, J., Coste, M., Roy, M.F.: Géométrie Algébrique Réelle. Springer, Heidelberg (1987)

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. Chandra, A., Harel, D.: Structure and complexity of relational queries. Journal of Computer and System Sciences 25, 99–128 (1982)

    Article  MATH  Google Scholar 

  6. Ebbinghaus, H.-D., Flum, J., Thomas, W.: Mathematical Logic. In: Undergraduate Texts in Mathematics. Springer, Heidelberg (1984)

    Google Scholar 

  7. Egenhofer, M.: Reasoning about binary topological relations. In: Günther, O., Schek, H.-J. (eds.) SSD 1991. LNCS, vol. 525, pp. 143–160. Springer, Heidelberg (1991)

    Google Scholar 

  8. Egenhofer, M.: Topological relations between regions in R2 and Z2. In: Abel, D.J., Ooi, B.-C. (eds.) SSD 1993. LNCS, vol. 692, pp. 316–336. Springer, Heidelberg (1993)

    Google Scholar 

  9. Egenhofer, M., Franzosa, R.: On the equivalence of topological relations. International Journal Geographical Information Systems, 523–542 (1994)

    Google Scholar 

  10. Forlizzi, L., Nardelli, E.: Some results on the modelling of spatial data. In: Rovan, B. (ed.) SOFSEM 1998. LNCS, vol. 1521, pp. 332–343. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  11. Forlizzi, L., Nardelli, E.: Characterization results for the poset based representation of topological relations-I: Introduction and models. Informatica (Slovenia) 23(2), 332–343 (1999)

    MathSciNet  Google Scholar 

  12. Geerts, F., Kuijpers, B.: Linear approximation of planar spatial databases using transitive-closure logic. In: Proceedings of the 19th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS 2000), pp. 126–135 (2000)

    Google Scholar 

  13. Giannella, C., Van Gucht, D.: Adding a path connectedness operator to FO+poly (linear). Acta Informatica 38(9), 621–648 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Grumbach, S., Kuper, G.: Tractable recursion over geometric data. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 450–462. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  15. Heintz, J., Roy, M.-F., Solernó, P.: Description of the connected components of a semialgebraic set in single exponential time. Discrete and Computational Geometry 6, 1–20 (1993)

    Google Scholar 

  16. Kainz, W.: Spatial relationships-topology versus order. In: Proceedings of the 4th International Symposium on Spatial Data Handling, vol. 2, pp. 814–819 (1990)

    Google Scholar 

  17. Kainz, W., Egenhofer, M., Greasley, I.: Modelling spatial relations and operations with partially ordered sets. International Journal of Geographical Information Systems 7(3), 215–229 (1993)

    Article  Google Scholar 

  18. Kreutzer, S.: Fixed-point query languages for linear constraint databases. In: Proceedings of the 19th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS 2000), pp. 116–125 (2000)

    Google Scholar 

  19. Kuijpers, B.: Topological Properties of Spatial Databases in the Polynomial Constraint Model. PhD thesis. University of Antwerp, UIA (1998)

    Google Scholar 

  20. Kuijpers, B., Paredaens, J., Smits, M., Van den Bussche, J.: Termination properties of spatial Datalog programs. In: Pedreschi, D., Zaniolo, C. (eds.) LID 1996. LNCS, vol. 1154, pp. 101–116. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  21. Kuijpers, B., Paredaens, J., Van den Bussche, J.: Lossless representation of topological spatial data. In: Egenhofer, M.J., Herring, J.R. (eds.) SSD 1995. LNCS, vol. 951, pp. 1–13. Springer, Heidelberg (1995)

    Google Scholar 

  22. Kuijpers, B., Paredaens, J., Van den Bussche, J.: Topological elementary equivalence of closed semi-algebraic sets in the real plane. The Journal of Symbolic Logic 65(4), 1530–1555 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  23. Kuijpers, B., Van den Bussche, J.: On capturing first-order topological properties of planar spatial databases. In: Beeri, C., Bruneman, P. (eds.) ICDT 1999. LNCS, vol. 1540, pp. 187–198. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  24. Kuijpers, B., Vianu, V.: Topological queries. In: Paredaens, J., Kuper, G., Libkin, L. (eds.) Constraint databases, ch. 2, pp. 231–274. Springer, Heidelberg (2000)

    Google Scholar 

  25. Papadimitriou, C.H., Suciu, D., Vianu, V.: Topological queries in spatial databases. Journal of Computer and System Sciences 58(1), 29–53 (1999); An extended abstract appeared in PODS 1996

    Article  MATH  MathSciNet  Google Scholar 

  26. Paredaens, J., Kuper, G., Libkin, L. (eds.): Constraint databases. Springer, Heidelberg (2000)

    MATH  Google Scholar 

  27. Pratt, I.: First-order qualitative spatial representation languages with convexity. Spatial Cognition and Computation 1, 181–204 (1999)

    Article  Google Scholar 

  28. Pratt, I., Lemon, O.: Ontologies for plane, polygonal mereotopology. Notre Dame Journal of Formal Logic 38(2), 225–245 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  29. Pratt, I., Schoop, D.: A complete axiom system for polygonal mereotopology of the real plane. Journal of Philosophical Logic 27(6), 621–661 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  30. Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. In: Principles of Knowledge Representation and Reasoning: Proceedings of the 3rd International Conference (KR 1992), pp. 165–176. Morgan Kaufmann, San Francisco (1992)

    Google Scholar 

  31. Revesz, P.: Introduction to Constraint Databases. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  32. Segoufin, L., Vianu, V.: Querying spatial databases via topological invariants. Journal of Computer and System Sciences 61(2), 270–301 (2000); An extended abstract appeared in PODS 1998

    Article  MATH  MathSciNet  Google Scholar 

  33. Stillwell, J.: Classical Topology and Combinatorial Group Theory. Graduate Texts in Mathematics, vol. 72. Springer, Heidelberg (1980)

    Google Scholar 

  34. Talamo, M., Vocca, P.: A data structure for lattice representation. Theoretical Computer Science 175(2), 373–392 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  35. Ullman, J.: Principles of Database and Knowledge-Base Systems, vol. I and II. Computer Science Press, Rockville (1989)

    Google Scholar 

  36. Van den Bussche, J., Cabibbo, L.: Converting untyped formulas to typed ones. Acta Informatica 35(8), 637–643 (1998)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, University of L’Aquila, Via Vetoio, 67010, L’Aquila, Italy

    Luca Forlizzi & Enrico Nardelli

  2. Dept. of Mathematics, Physics and Computer Science, University of Limburg, 3590, Diepenbeek, Belgium

    Bart Kuijpers

  3. IASI–CNR, Viale Manzoni 30, 00185, Roma, Italy

    Enrico Nardelli

Authors
  1. Luca Forlizzi
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  2. Bart Kuijpers
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  3. Enrico Nardelli
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Editor information

Editors and Affiliations

  1. Research Academic Computer Technology Institute, Patras, Greece

    Thanasis Hadzilacos

  2. Data Engineering Research Lab. Department of Informatics,, Aristotle University, 54124, Thessaloniki, Greece

    Yannis Manolopoulos

  3. Flinders University, Adelaide, Australia

    John Roddick

  4. Department of Informatics, University of Piraeus, Greece

    Yannis Theodoridis

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© 2003 Springer-Verlag Berlin Heidelberg

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Forlizzi, L., Kuijpers, B., Nardelli, E. (2003). Region-Based Query Languages for Spatial Databases in the Topological Data Model. In: Hadzilacos, T., Manolopoulos, Y., Roddick, J., Theodoridis, Y. (eds) Advances in Spatial and Temporal Databases. SSTD 2003. Lecture Notes in Computer Science, vol 2750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45072-6_20

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  • DOI: https://doi.org/10.1007/978-3-540-45072-6_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40535-1

  • Online ISBN: 978-3-540-45072-6

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