Topological Canonization of Planar Spatial Data and its Incremental Maintenance

  • Floris Geerts
  • Bart Kuijpers
  • Jan Van den Bussche
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 496)


It is known that to a planar spatial database, represented by a semi-algebraic set in the plane, one can associate a structure, here called the “topological canonization”, such that two databases are topologically equivalent if and only if their topological canonizations are isomorphic. The advantage of a topological canonization is that it contains precisely the information one needs if one is only interested in topological properties of the spatial data. In this paper we represent semi-algebraic sets using plane graph structures. Canonizations are represented by plane graph structures as well (the so-called canonical structures). We discuss the basic properties of canonical structures and of canonization. We then present a method for incremental maintenance of the canonization under elementary updates on the original spatial database. Incremental maintenance takes less time than recomputing the canonization from scratch.


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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Floris Geerts
    • 1
  • Bart Kuijpers
    • 2
  • Jan Van den Bussche
    • 1
  1. 1.University of Limburg (LUC)Belgium
  2. 2.University of Antwerp (UIA)Belgium

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