## Abstract

Current database systems cannot only store standard data like \(\underline{integer}\), \(\underline{string}\), and \(\underline{real}\) values, but also spatial data like \(\underline{points}\), \(\underline{lines}\), and \(\underline{regions}\). The importance of topological relationships between spatial objects has been recognized a long time ago. Using the well known 9-intersection model for describing such relationships, a lot of different topological relationships can be distinguished. For the query language of a database system it is not desirable to have such a large number of topological predicates. Particularly the query language should not be extended by a lot of predicate names. It is desirable to build new relationships from existing ones, for example to coarse the granularity. This paper describes how a database system user can define and use her own topological predicates. We show algorithms for computing such predicates in an efficient way. Last, we compare these general versions with specialized implementations of topological predicates.

## Keywords

Topological predicate Topological relationships Spatial database User defined topological predicate## References

- 1.Clementini E, di Felice P (1996) A model for representing topological relationships between complex geometric features in spatial databases. Inf Sci 90(1–4):121–136CrossRefGoogle Scholar
- 2.Clementini E, Di Felice P, Califano G (1995) Composite regions in topological queries. IS 20(7):579–594Google Scholar
- 3.Clementini E, Felice PD (1993) An object calculus for geographic databases. In: SAC ’93: Proceedings of the 1993 ACM/SIGAPP symposium on applied computing. New York, NY, USA, ACM, pp 302–308CrossRefGoogle Scholar
- 4.Clementini E, Felice PD, van Oosterom P (1993) A small set of formal topological relationships suitable for end-user interaction. In: SSD: advances in spatial databases. LNCS, SpringerGoogle Scholar
- 5.Egenhofer M, Clementini E, Di Felice P (1994) Topological relations between regions with holes. Int J Geographic Inf Syst 8(2):128–142Google Scholar
- 6.Egenhofer MJ (1989) A formal definition of binary topological relationships. In: Litwin W, Schek H (eds) Third international conference on foundations of data organization and algorithms (FODO). Lecture Notes in Computer Science, vol 367. Springer, pp 457–472, JuneGoogle Scholar
- 7.Egenhofer MJ, Herring JR (1990) Categorizing binary topological relations between regions, lines, and points in geographic databases. Technical report, Department of Surveying Engineering, University of Maine, MaineGoogle Scholar
- 8.Gaal SA (1964) Point set topology. Academic, New YorkGoogle Scholar
- 9.Güting RH (1993) Second-order signature: a tool for specifying data models, query processing, and optimization. In: Proc. of the ACM SIGMOD international conf. on management of data, pp 277–286Google Scholar
- 10.Güting RH, Behr T, Almeida V, Ding Z, Hoffmann F, Spiekermann M (2004) SECONDO: an extensible dbms architecture and prototype. Technical report, FernUniversität HagenGoogle Scholar
- 11.Güting RH, de Almeida VT, Ansorge D, Behr T, Ding Z, Höse T, Hoffmann F, Spiekermann M, Telle U (2005) SECONDO: an extensible dbms platform for research prototyping and teaching. In: ICDE. IEEE Computer Society, pp 1115–1116Google Scholar
- 12.Güting RH, Ding Z (2004) A simple but effective improvement to the plumb-line algoritm. Inf Process Lett 91(6):251–257CrossRefGoogle Scholar
- 13.Güting RH, Schneider M (1995) Realm-based spatial data types: the ROSE algebra. VLDB J 4(2):243–286CrossRefGoogle Scholar
- 14.Kothuri R, Godfrind A, Beinat E (2007) Pro oracle spatial for oracle database 11g. Springer, New YorkGoogle Scholar
- 15.Open GIS Consortium, Inc. (1999) OpenGIS simple features specification for SQL Revision 1.1, OpenGIS Project Document 99-049, MayGoogle Scholar
- 16.OpenGeoDB (2008) OpenGeoDB. http://opengeodb.hoppe-media.com, 2008-02-14
- 17.Reasey Praing MS (2008) Efficient implementation techniques for topological predicates on complex spatial objects. GeoInformatica 12(3):313–356CrossRefGoogle Scholar
- 18.Schneider M (2002) Implementing topological predicates for complex regions. In: Proceedings of the international symposium on spatial data handling, pp 313–328Google Scholar
- 19.Schneider M (2004) Computing the topological relationship of complex regions. In: DEXA, pp 844–853Google Scholar
- 20.Schneider M, Behr T (2006) Topological relationships between complex spatial objects. ACM Trans Database Syst 31(1):39–81CrossRefGoogle Scholar
- 21.Shamos MI, Hoey D (1976) Geometric intersection problems. In: FOCS. IEEE, pp 208–215Google Scholar
- 22.Stonebraker M, Frew J, Gardels K, Meredith J (1993) The sequoia 2000 benchmark. In: Buneman P, Jajodia S (eds) Proceedings of the 1993 ACM SIGMOD international conference on management of data. Washington, D.C., 26–28 May, ACM, New York, pp 2–11CrossRefGoogle Scholar