Abstract
This work is a contribution to the developing literature on multi-resolution data models. It considers operations for model-oriented generalization in the case where the underlying data is structured as a graph. The paper presents a new approach in that a distinction is made between generalizations that amalgamate data objects and those that select data objects. We show that these two types of generalization are conceptually distinct, and provide a formal framework in which both can be understood. Generalizations that are combinations of amalgamation and selection are termed simplifications, and the paper provides a formal framework in which simplifications can be computed (for example, as compositions of other simpliffcations). A detailed case study is presented to illustrate the techniques developed, and directions for further work are discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D.J. Abel. Spatial internet marketplaces: A grand challenge. In Proceedings 5th International Symposium SSD’97, volume 1262 of Lecture Notes in Computer Science, pages 3–8. Springer-Verlag, 1997.
M. Bertolotto. Geometric modeling of spatial entities at multiple levels of resolution. PhD thesis, Dipartmento di Informatica e Scienze dell Informazione, Universita di Genova, 1998.
L. Becker and R. H. Güting. The GraphDB Algebra: Specification of Advanced Data Models with Second-Order Signature. Informatik Berichte 183, FernUniversität, Hagen, May 1995.
B. Buttenfield and R. McMaster. Map Generalisation: Making Rules for Knowledge Representation. Longman, London, 1991.
T. Bittner and J.G. Stell. A boundary-sensitive approach to qualitative location. Annals of Mathematics and Artificial Intelligence, 24:93–114, 1998.
M. Barr and C. Wells. Category Theory for Computing Science. Prentice Hall, second edition, 1995.
M. Erwig and R.H. Güting. Explicit graphs in a functional model for spatial databases. IEEE Transactions on Knowledge and Data Engineering, 5:787–804, 1994.
M. Erwig and M. Schneider. Partition and conquer. In Hirtle and Frank [HF97], pages 389–407.
R.H. Güting. Extending a spatial database system by graphs and object class hierarchies. In G. Gambosi, M. Scholl, and H. Six, editors, Proc. Int. Workshop on Geographic Database Management Systems, pages 34–55. Springer-Verlag, 1992.
R.H. Güting. GraphDB: A Data Model and Query Language for Graphs in Databases. Informatik Berichte 155-2/1994, FernUniversität, Hagen, 1994.
S.C. Hirtle and A. U. Frank, editors. Spatial Information Theory, International Conference COSIT’97, Proceedings, volume 1329 of Lecture Notes in Computer Science. Springer-Verlag, 1997.
J.C. Müller et al. Generalization-state of the art and issues. In J.C. Müller, J.P. Lagrange, and R. Weibel, editors, GIS and Generalisation: Methodology and Practice, pages 3–17. Taylor and Francis, London, 1995.
J.C. Müller, J. P. Lagrange, and R. Weibel, editors. GIS and Generalisation: Methodology and Practice. Taylor and Francis, London, 1995.
M. Mannino and L. Shapiro. Extensions to query languages for graph traversal problems. IEEE Transactions on Knowledge and Data Engineering, 2:353–363, 1990.
E. Puppo and G. Dettori. Towards a formal model for multiresolution spatial maps. In Advances in Spatial Databases SSD’95, volume 951 of Lecture Notes in Computer Science, pages 152–169. Springer-Verlag, 1995.
P. Rigaux and P. Scholl. Multi-scale partitions: Applications to spatial and statistical databases. In Advances in Spatial Databases SSD′95, volume 951 of Lecture Notes in Computer Science, pages 170–183. Springer-Verlag, 1995.
J.G. Stell. Granularity for graphs. In Proceedings of Conference on Spatial Information Theory, COSIT′99, Lecture Notes in Computer Science. Springer-Verlag, to appear 1999.
J.G. Stell and M. F. Worboys. The algebraic structure of sets of regions. In Hirtle and Frank [HF97], pages 163–174.
J.G. Stell and M. F. Worboys. Stratified map spaces: A formal basis for multi-resolution spatial databases. In T. K. Poiker and N. Chrisman, editors, SDH’98 Proceedings 8th International Symposium on Spatial Data Handling, pages 180–189. International Geographical Union, 1998.
M.F. Worboys. Computation with imprecise geospatial data. Computers, Environment and Urban Systems, 22:85–106, 1998.
M.F. Worboys. Imprecision in finite resolution spatial data. GeoInformatica, 2:257–279, 1998.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Stell, J.G., Worboys, M.F. (1999). Generalizing Graphs Using Amalgamation and Selection. In: Güting, R.H., Papadias, D., Lochovsky, F. (eds) Advances in Spatial Databases. SSD 1999. Lecture Notes in Computer Science, vol 1651. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48482-5_4
Download citation
DOI: https://doi.org/10.1007/3-540-48482-5_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66247-1
Online ISBN: 978-3-540-48482-0
eBook Packages: Springer Book Archive