Querying spatial databases via topological invariants

Journal of Computer and System Sciences

Volumn 61, Issue 2, 2000, Pages 270-301

  Segoufin, Luc ^a   Vianu, Victor ^b  

^a INRIA   (France)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER AIDED DESIGN; COMPUTER AIDED MANUFACTURING; GEOGRAPHIC INFORMATION SYSTEMS; INFORMATION SCIENCE; MEDICAL IMAGING; QUERY LANGUAGES; ROBOTICS; TOPOLOGY;

ANNOTATIONS; TOPOLOGICAL INVARIANTS;

DISTRIBUTED DATABASE SYSTEMS;

EID: 0034297699     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.2000.1712     Document Type: Article

References (53)

1. Abiteboul S., Hull R., Vianu V. Foundations of Databases. 1995;Addison-Wesley, Reading.
2. Abiteboul S., Vianu V. Computing with first-order logic. J. Comput. System Sci. 50:1995;309-335.
3. Benedikt M., Dong G., Libkin L., Wong L. Relational expressive power of constraint query languages. Assoc. Comput. Mach. 45:1998;1-34.
4. Ben-Or M., Kozen D., Reif J. The complexity of elementary algebra and geometry. J. Comput. System Sci. 32:1986;251-264.
5. Cai J., Fürer M., Immerman N. An optimal lower boundon the number of variables for graph identification. Combinatorica. 12:1992;389-410.
6. Corbett J. P. Topological Principles in Cartography. Technical Paper 48. 1979;US Bureau of the Census, Washington D.C.
7. Crowell R., Fox R. Introduction to Knot Theory. Graduate Texts in Mathematics. 57:1963;Springer-Verlag, Berlin/New York.
8. Dawar A., Lindell S., Weinstein S. Infinitary logic and inductive definability over finite structures. Inform. and Comput. 119:1995;160-175.
9. Egenhofer M. A model for detailed binary topological relationships. Geomatica. 47:1993;261-273.
10. Egenhofer M. J., Franzosa R. Point-set topological spatial relations. Internat. J. Geogr. Inform. Systems. 5:1991;161-174.
11. Egenhofer M., Franzosa R. On the equivalence of topological relations. Internat. J. Geogr. Inform. Systems. 9:1995;133-152.
12. Ebbinghaus H.-D., Flum J. Finite Model Theory. 1995;Springer-Verlag, Berlin/New York.
13. R. Franzosa and M. Egenhofer, Topological spatial realtions based on components and dimensions of set intersections, in Proc. SPIE's OE/Technology '92-Vision Geometry, Boston, MA, 1992 (R. Melter and A. Wu, Eds.), pp. 236-246.
14. Egenhofer M. Spatial SQL: A query and presentation language. IEEE Trans. Knowledge Data Engrg. 6:1994;86-95.
15. A. Frank and W. Kuhn, Cell graph: A provable correct method for the storage of geometry, in Proc. Second International Symposium on Spatial Data Handling, Seattle, WA, 1986 (D. Marble, Ed.), pp. 411-436.
16. Fagin R., Stockmeyer L., Vardi M. On monadic NP vs. monadic co-NP. Inform. and Comput. 120:1995;78-92.
17. Grädel E., Otto M. Inductive definability with counting on finite structures. Börger E. Computer Science Logic, CSL'92 Selected Papers. Lecture Notes in Computer Science. 702:1993;231-247 Springer-Verlag, Berlin/New York.
18. M. Grigni, D. Papadias, and, C. H. Papadimitriou, Topological inference, IJCAI, 1995.
19. k-types. Proc. Symp. on Logic in Computer Science. 1997;. p. 216-227.
20. Grohe M. Fixed-point logics on planar graphs. Proc. Symp. on Logic in Computer Science. 1998;. p. 6-15.
21. M. Grohe, and, L. Segoufin, personal communication, 1999.
22. Grumbach S., Kuper G. Tractable recursion over geometric data. Proc. Int'l Conf. on Constraint Programming. 1997;. p. 450-462.
23. Grumbach S., Su J. Queries with arithmetical constraints. Theoret. Comput. Sci. 173:1997;151-181.
24. Grumbach S., Su J. Finitely representable databases. J. Comput. System. Sci. 55:1997;273-298.
25. Grumbach S., Su J., Tollu C. Linear constraint databases. Leivant D. Proc. Logic and Complexity Workshop. 1994.
26. Gurevich Y. Toward logic tailord for computational complexity. Ricther M. M. Computation and Proof Theory. Lecture Notes in Mathematics. 1104:1984;175-216 Springer-Verlag, Berlin/New York.
27. Gurevich Y. Logic and the challenge of computer science. Borger E. Trends in Theoretical Computer Science. 1988;1-57 Computer Science Press.
28. Herring J. TIGRIS: A data model for an object-oriented geographic information system. Comput. Geosc. 18:1991;443-452.
29. La Base de Donneés Topographiques de l'I.G.N. (The Cartographical Database of the National Geographic Institute) Bulletin d'Information de l'I.G.N. 59, 1991. [In French].
30. Immerman N. Relational queries computable in polynomial time. Inform. and Control. 68:1986;86-104.
31. Immerman N. Expressibility as a complexity measure: results and directions. Proc. 2nd Structure in Complexity Conference. 1987;. p. 194-202.
32. Kanellakis P. C., Kuper G. M., Revesz P. Z. Constraint query languages. J. Comput. System Sci. 51:1995;26-52.
33. D. Kozen and C.-K. Yap, Algebraic Cell Decomposition in NC, in Proc. IEEE Symp. on Foundations of Computer Science, 1985, pp. 515-521.
34. Kuijpers B., Paredaens J., Van den Bussche J. Lossless representation of topological spatial data. Proc. Fourth Int'l Symp. on Large Spatial Databases. 1995;. p. 1-13.
35. B. Kuijpers, J. Paredaens, and J. Van den Bussche, On topological elementary equivalence of spatial databases, in Proc. Int'l Conf. on Database Theory, 1997, pp. 432-446.
36. Morehouse S. ARC/INFO: A geo-relational model for spatial information. Proc. Int'l Symp. on Computer Assisted Cartography (Auto-Carto 7). 1985;. p. 388-397.
37. Morehouse S. The architecture of ARC/INFO. Proc. Int'l Symp. on Computer Assisted Cartography (Auto-Carto 9). 1989;. p. 266-277.
38. A. A. Markov, Unsolvability of the problem of homeomorphy, in Proc. Int'l Congress of Mathematics, 1958, pp. 300-306. [In Russian].
39. P. van Oosterom and T. Vijlbrief, Building a GIS on top of the open DBMS Postgres, EGIS '91, Brussels Belgium, 1991, pp. 775-787.
40. Papadimitriou C. H., Suciu D., Vianu V. Topological queries in spatial databases. J. Comput. System Sci. 58:1999;29-53.
41. J. Paredaens, J. Van Den Bussche, and D. Van Gucht, Towards a theory of spatial database queries, in Proc. ACM Symp. on Principles of Database Systems, 1994, pp. 279-288.
42. J. Paredaens, Spatial databases, the final frontier, in Proc. 5th Int'l Conf. on Database Theory, 1995, pp. 14-32.
43. Paredaens J., Van Den Bussche J., Van Gucht D. First-order queries on finite structures over the reals. Proc. IEEE Conf. on Logic in Computer Science. 1995;. p. 79-87.
44. Renegar J. On the computational complexity and geometry of the first-order theory of the reals. J. Symbolic Comput. 13:1992;255-300.
45. Rosenstein J. G. Linear Orderings. 1982;Academic Press, San Diego.
46. Rozenberg G., Salomaa A. Handbook of Formal Languages. 1997;Springer-Verlag, Berlin/New York.
47. Segoufin L. Manipulation de donneés spatiales et topologiques. January 1999;Université d'Orsay.
48. Stonebraker M., Frew J., Gardels K., Meredith J. The Sequoia 2000 storage benchmark. Proc ACM SIGMOD Int'l Conf. on the Management of Data. 1993;. p. 2-11.
49. Svensson P., Zhexue H. Geo-SAL: A query language for spatial data analysis. Günther O., Schek H.-J. Proc. Advances in Spatial Databases-Second Symposium, SSD '91. Lecture Notes in Computer Science. 525:1991;119-140 Springer-Verlag, New York.
50. Tarski A. A Decision Method for Elementary Algebra and Geometry. 1951;University of California Press, Berkeley.
51. T. Wilke, personal communication, 1998.
52. Vardi M. Y. The complexity of relational query languages. Proc. 14th ACM Symp. on Theory of Computing. 1982;. p. 137-146.
53. Worboys M. A geometric model for planar geographical objects. Internat. J. Geogr. Inform. Systems. 6:1992;353-372.