The Maptree: A Fine-Grained Formal Representation of Space

  • Michael Worboys
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7478)


This paper introduces a new formal structure, called the maptree, that is shown to uniquely specify, up to homeomorphism, the topological structure of embeddings of graphs in orientable, closed surfaces. A simple modification is made to show that the representation also works for planar embeddings. It is shown that the maptrees are capable of providing a rich representation of the topology of 2D spatial objects and their relationships. The maptree representation is then used to characterize some properties of topological change in these embeddings.


maptree topology topological change geographic information science theory 


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  1. 1.
    Buneman, O.P.: A grammar for the topological analysis of plane figures. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence, vol. 5, pp. 383–393. Elselvier (1970)Google Scholar
  2. 2.
    Edmonds, J.R.: A combinatorial representation for polyhedral surfaces. Notices Amer. Math. Soc. 7, 646 (1960)Google Scholar
  3. 3.
    Egenhofer, M.J., Franzosa, R.D.: Point-set topological spatial relations. International Journal of Geographical Information Systems 5(2), 161–174 (1991)CrossRefGoogle Scholar
  4. 4.
    Jiang, J., Nittel, M., Worboys, S.: Qualitative change detection using sensor networks based on connectivity information. GeoInformatica 15(2), 305–328 (2011)CrossRefGoogle Scholar
  5. 5.
    Jiang, J., Worboys, M.: Event-based topology for dynamic planar areal objects. International Journal of Geographical Information Science 23(1), 33–60 (2009)CrossRefGoogle Scholar
  6. 6.
    Randell, D.A., Cui, Z., Cohn, A.: A spatial logic based on regions and connection. In: Nebel, B., Rich, C., Swartout, W. (eds.) KR 1992. Principles of Knowledge Representation and Reasoning: Proceedings of the Third International Conference, pp. 165–176. Morgan Kaufmann, San Mateo (1992)Google Scholar
  7. 7.
    Stell, J., Worboys, M.: Relations between adjacency trees. Journal of Theoretical Computer Science 412, 4452–4468 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Tutte, W.T.: What is a map? In: New Directions in the Theory of Graphs, pp. 309–325. Academic Press, New York (1973)Google Scholar
  9. 9.
    Worboys, M.F.: Event-oriented approaches to geographic phenomena. International Journal of Geographic Information Science 19(1), 1–28 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Michael Worboys
    • 1
  1. 1.School of Computing and Information ScienceUniversity of MaineOronoUSA

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