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Topological Queries

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Constraint Databases

Abstract

As discussed in Chapter 8, there are applications for which the precise size of the regions is not important, but rather the topological relationships between them are of primary interest. Such differences in scope and emphasis are crucial, as they affect the data model, the query language, and performance. This chapter presents a survey of results concerning topological queries in spatial databases. Motivated primarily by GIS, we focus on semi-algebraic regions in the two-dimensional plane.

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Bibliographic Notes

  1. B. Kuijpers, J. Paredaens, and J. Van den Bussche. Lossless representation of topological spatial data. In 4th Symposium on Large Spatial Databases (SSD’95), volume 951 of Lecture Notes in Computer Science, pages 1–13. Springer-Verlag, 1995.

    Google Scholar 

  2. C. H. Papadimitriou, D. Suciu, and V. Vianu. Topological queries in spatial databases. In Proceedings of the 15th ACM SIGACTSIGMOD-SIGART Symposium on Principles of Database Systems (PODS’96)pages 81–92. ACM Press, 1996.

    Google Scholar 

  3. L. Segoufin and V. Vianu. Querying spatial databases via topological invariants. In Proceedings of the 17th ACM SIGACT-SIGMODSIGART Symposium on Principles of Database Systems (PODS’98), pages 89–98. ACM Press, 1998.

    Google Scholar 

  4. M. Grigni, D. Papadias, and C. H. Papadimitriou. Topological inference. In Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI 95), pages 901–907. Morgan Kaufmann, 1995.

    Google Scholar 

  5. C. H. Papadimitriou, D. Suciu, and V. Vianu. Topological queries in spatial databases. In Proceedings of the 15th ACM SIGACTSIGMOD-SIGART Symposium on Principles of Database Systems (PODS’96)pages 81–92. ACM Press, 1996.

    Google Scholar 

  6. B. Kuijpers, J. Paredaens, and J. Van den Bussche. Lossless representation of topological spatial data. In 4th Symposium on Large Spatial Databases (SSD’95), volume 951 of Lecture Notes in Computer Science, pages 1–13. Springer-Verlag, 1995.

    Google Scholar 

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

    Google Scholar 

  8. L. Segoufin. Manipulation de Données Spatiales et Topologiques. PhD thesis, University of Paris, Orsay, 1998.

    Google Scholar 

  9. R. H. Crowell and R. H. Fox. Introduction to Knot Theory. Number 57 in Graduate Texts in Mathematics. Springer-Verlag, 1963.

    Google Scholar 

  10. A. A. Markov. Unsolvability of the problem of homeomorphy. In International Congress of Mathematics,pages 300–306, 1958. In Russian.

    Google Scholar 

  11. L. Segoufin and V. Vianu. Querying spatial databases via topological invariants. In Proceedings of the 17th ACM SIGACT-SIGMODSIGART Symposium on Principles of Database Systems (PODS’98), pages 89–98. ACM Press, 1998.

    Google Scholar 

  12. M. Stonebraker, J. Frew, K. Gardels, and J. Meredith. The SEQUOIA 2000 benchmark. In Proceedings of the 1993 ACM SIGMOD International Conference on Management of Data (SIGMOD’93), pages 2–11. ACM Press, 1993.

    Google Scholar 

  13. IGN. La base de données topographiques de l’IGN. (The cartographical database of the national geographic institute), in French. Technical Report 59, Bulletin d’Information de l’IGN., 1991.

    Google Scholar 

  14. L. Segoufin and V. Vianu. Querying spatial databases via topological invariants. In Proceedings of the 17th ACM SIGACT-SIGMODSIGART Symposium on Principles of Database Systems (PODS’98), pages 89–98. ACM Press, 1998.

    Google Scholar 

  15. M. Grohe. Fixed-point logics on planar graphs. In Proceedings 13 th IEEE Symposium on Logic in Computer Science (LICS’98), pages 6–15, 1998.

    Google Scholar 

  16. R. Laurini and D. Thompson. Fundamentals of Spatial Information Systems. Number 37 in The A.P.I.C. Series. Academic Press, 1992.

    Google Scholar 

  17. R. H. Giiting. An introduction to spatial database systems. The VLDB Journal, 3 (4): 357–399, 1994.

    Article  Google Scholar 

  18. A. U. Frank and W. Kuhn. Cell graph: A provable correct method for the storage of geometry. In Proceedings of the 2nd International Symposium on Spatial Data Handling (SDH’86), pages 411–436, 1986.

    Google Scholar 

  19. J. R. Herring. TIGRIS: A data model for an object-oriented geographic information system. Computers and Geosciences, 18 (4): 443–452, 1991.

    Article  Google Scholar 

  20. M. F. Worboys. A generic model for planar geographical objects. International Journal of Geographical Information Systems, 6 (5): 353–372, 1992.

    Article  Google Scholar 

  21. M. Grigni, D. Papadias, and C. H. Papadimitriou. Topological inference. In Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI 95), pages 901–907. Morgan Kaufmann, 1995.

    Google Scholar 

  22. Z. Chen, M. Grigni, and C. H. Papadimitriou. Planar map graphs. In Proceedings of the 30th ACM Symposium on Theory of Computing (STOC’86), pages 514–523, 1998.

    Google Scholar 

  23. C. H. Papadiinitriou. Planar topological queries. In Proceedings of the 2nd Workshop on Constraint Databases and Applications (CDB’97), volume 1191 of Lecture Notes in Computer Science, pages 1–6. Springer-Verlag, 1997.

    Google Scholar 

  24. J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In Proceedings of the 13th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS’94), pages 279–288. ACM Press, 1994.

    Google Scholar 

  25. B. Kuijpers, J. Paredaens, and J. Van den Bussche. On topological elementary equivalence of spatial databases. In 6th International Conference on Database Theory (ICDT’97), volume 1186 of Lecture Notes in Computer Science, pages 432–446. Springer-Verlag, 1997.

    Google Scholar 

  26. B. Kuijpers and J. Van den Bussche. On capturing first-order topological properties of planar spatial databases. In 7th International Conference on Database Theory (ICDT’99), volume 1540 of Lecture Notes in Computer Science, pages 187–198. Springer-Verlag, 1999.

    Google Scholar 

  27. S. Morehouse. ARC/INFO: A geo-relational model for spatial information. In Proceedings of the International Symposium on Computer Assisted Cartography (Auto-Carto 7), pages 388–397, 1985.

    Google Scholar 

  28. S. Morehouse. The architecture of ARC/INFO. In Proceedings of the Auto Carto 9 Conference, pages 266–277. American Society for Photogrammetry and Remote Sensing/American Congress for Surveying and Mapping, 1989.

    Google Scholar 

  29. M. J. Egenhofer. Spatial SQL: A query and presentation language. IEEE Transactions on Knowledge and Data Engineering (TKDE), 6 (1): 86–95, 1994.

    Article  Google Scholar 

  30. P. van Oosterom and T. Vijlbrief. Building a GIS on top of the open dbms postgres. In EGIS’91, pages 775–787, 1991.

    Google Scholar 

  31. P. Svensson and Z. Huang. Geo-SAL: A query language for spatial data analysis. In 2nd Symposium on Large Spatial Databases (SSD’91), volume 525 of Lecture Notes in Computer Science, pages 119–140. Springer-Verlag, 1991.

    Google Scholar 

  32. M. J. Egenhofer and R. D. Franzosa. Point-set topological spatial relations. International Journal of Geographical Information Systems, 5 (2): 161–174, 1991.

    Article  Google Scholar 

  33. R. D. Franzosa and M. J. Egenhofer. Topological spatial relations based on components and dimensions of set intersections. In SPIE’s OE/Technology ‘82-Vision Geometry, pages 236–246, Boston, MA, 1992.

    Google Scholar 

  34. M. J. Egenhofer. A model for detailed binary topological relationships. Geomatica, 47 (3/4): 261–273, 1993.

    Google Scholar 

  35. M. J. Egenhofer and R. D. Franzosa. On the equivalence of topological relations. International Journal of Geographical Information Systems, 9 (2): 133–152, 1995.

    Article  Google Scholar 

  36. J. P. Corbett. Topological principles in cartography. Technical report, Technical Paper 48, US Bureau of the Census, Washington DC, 1979.

    Google Scholar 

  37. R. Laurini and D. Thompson. Fundamentals of Spatial Information Systems. Number 37 in The A.P.I.C. Series. Academic Press, 1992.

    Google Scholar 

  38. J. Paredaens. Spatial databases, the final frontier. In 5th International Conference on Database Theory (ICDT’95), volume 893 of Lecture Notes in Computer Science, pages 14–32. Springer-Verlag, 1995.

    Google Scholar 

  39. A. U. Frank and W. Kuhn. Cell graph: A provable correct method for the storage of geometry. In Proceedings of the 2nd International Symposium on Spatial Data Handling (SDH’86), pages 411–436, 1986.

    Google Scholar 

  40. J. R. Herring. TIGRIS: A data model for an object-oriented geographic information system. Computers and Geosciences, 18 (4): 443–452, 1991.

    Article  Google Scholar 

  41. M. F. Worboys. A generic model for planar geographical objects. International Journal of Geographical Information Systems, 6 (5): 353–372, 1992.

    Article  Google Scholar 

  42. D. Kozen and C.-K. Yap. Algebraic cell decomposition in NC. In Proceedings 26th IEEE Symposium on Foundations of Computer Science (FOCS’85), pages 515–521, 1985.

    Google Scholar 

  43. M. Ben-Or, D. Kozen, and J. H. Reif. The complexity of elementary algebra and geometry. Journal of Computer and System Sciences (JCSS), 32 (2): 251–264, 1986.

    Article  MATH  Google Scholar 

  44. J. Renegar. On the computational complexity and geometry of the first-order theory of the reals, parts I—III. Journal of Symbolic Computation (JSC), 13: 255–352, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  45. J. Bochnak, M. Coste, and M.-F. Roy. Real Algebraic Geometry, volume 36 of Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge. Springer-Verlag, 1998.

    Google Scholar 

  46. N. Immerman. Relational queries computable in polynomial time. Information and Control, 68 (1–3): 86–104, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  47. M. Y. Vardi. The complexity of relational query languages. In Proceedings of the 14th ACM Symposium on Theory of Computing (STOC’82), pages 137–146, 1982.

    Google Scholar 

  48. J.-Y. Cai, M. Fürer, and N. Immerman. An optimal lower bound on the number of variables for graph identification. Combinatorica, 12: 389–410, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  49. E. Grädel and M. Otto. Inductive definability with counting on finite structures. In 6th Workshop on Computer Science Logic (CSL’92), volume 832 of Lecture Notes in Computer Science, pages 231–247. Springer-Verlag, 1993.

    Google Scholar 

  50. S. Abiteboul and V. Vianu. Computing with first-order logic. Journal of Computer and System Sciences (JCSS), 50 (2): 309–335, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  51. A. Dawar, S. Lindell, and S. Weinstein Infinitary logic and inductive definability over finite structures. Information and Computation, 119(2): 160–175, 1995.

    Google Scholar 

  52. M. Grohe. Large finite structures with few Lk-types. In Proceedings 12th IEEE Symposium on Logic in Computer Science (LICS’97), pages 216–227, 1997.

    Google Scholar 

  53. Y. Gurevich. Toward logic tailored for computational complexity. In Computation and Proof Theory, volume 1104 of Lecture Notes in Mathematics, pages 175–216. Springer-Verlag, 1984.

    Google Scholar 

  54. S. Grumbach and G. M. Kuper. Tractable recursion over geometric data. In Proceedings of the and International Conference on Principles and Practice of Constraint Programming (CP’97), volume 1330 of Lecture Notes in Computer Science, pages 450–462. Springer-Verlag, 1997.

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  56. A. Tarski. A Decision Method for Elementary Algebra and Geometry. University of California Press, 1951.

    Google Scholar 

  57. S. Grumbach and J. Su. Finitely representable databases. In Proceedings of the 13th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS’94), pages 289–300. ACM Press, 1994.

    Google Scholar 

  58. S. Grumbach and J. Su. Dense-order constraint databases. In Proceedings of the 14th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS’95), pages 66–77. ACM Press, 1995.

    Google Scholar 

  59. B. Clark. A calculus of individuals based on `connection’. Notre Dame Journal of Formal Logic, 22 (3), 1985.

    Google Scholar 

  60. D. A. Randell and A. G. Cohn. Modeling topological and metrical properties in physical processes. In Proceedings of the 1st International Conference on Principles of Knowledge Representation and Reasoning (KR’89), pages 357–368. Morgan Kaufmann, 1989.

    Google Scholar 

  61. A. G. Cohn, D. A. Randell, and Z. Cui. Taxonomies of logically defined qualitative spatial relations. In N. Guarino and R. Poli, editors, Formal Ontology in Conceptual Analysis and Knowledge Representation. Kluwer Academic Publishers, 1994.

    Google Scholar 

  62. A. Ziegler. Topological model theory. In J. Barwise and S. Feferman, editors, Model-Theoretic Logics. Springer-Verlag, 1985.

    Google Scholar 

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Kuijpers, B., Vianu, V. (2000). Topological Queries. In: Kuper, G., Libkin, L., Paredaens, J. (eds) Constraint Databases. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04031-7_10

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  • DOI: https://doi.org/10.1007/978-3-662-04031-7_10

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