Abstract
This paper further develops the theory of maptrees, introduced in [13]. There exist well-known methods, based upon combinatorial maps, for topologically complete representations of embeddings of connected graphs in closed surfaces. Maptrees extend these methods to provide topologically complete representations of embeddings of possibly disconnected graphs. The focus of this paper is the use of maptrees to admit fine-grained representations of topological change. The ability of maptrees to represent complex spatial processes is demonstrated through case studies involving conceptual neighborhoods and cellular processes.
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References
Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Pardini, G., Tesei, L.: Spatial P systems. Natural Computing (2010)
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)
Cardelli, L.: Brane calculi. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 257–278. Springer, Heidelberg (2005)
Edmonds, J.R.: A combinatorial representation for polyhedral surfaces. Notices Amer. Math. Soc. 7, 646 (1960)
Egenhofer, M.J., Franzosa, R.D.: Point-set topological spatial relations. International Journal of Geographical Information Systems 5(2), 161–174 (1991)
Egenhofer, M.J., Mark, D.M.: Modeling conceptual neighborhoods of topological line-region relations. International Journal of Geographical Information Systems 9(5), 555–565 (1995)
Freksa, C.: Temporal reasoning based on semi-intervals. Artificial Intelligence 54, 199–227 (1992)
Jiang, J., Nittel, M., Worboys, S.: Qualitative change detection using sensor networks based on connectivity information. GeoInformatica 15(2), 305–328 (2011)
Jiang, J., Worboys, M.: Event-based topology for dynamic planar areal objects. International Journal of Geographical Information Science 23(1), 33–60 (2009)
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)
Stell, J., Worboys, M.: Relations between adjacency trees. Theoretical Computer Science 412, 4452–4468 (2011)
Tutte, W.T.: What is a map? In: New Directions in the Theory of Graphs, pp. 309–325. Academic Press, New York (1973)
Worboys, M.: The maptree: A fine-grained formal representation of space. In: Xiao, N., Kwan, M.-P., Goodchild, M.F., Shekhar, S. (eds.) GIScience 2012. LNCS, vol. 7478, pp. 298–310. Springer, Heidelberg (2012)
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Worboys, M. (2013). Using Maptrees to Characterize Topological Change. In: Tenbrink, T., Stell, J., Galton, A., Wood, Z. (eds) Spatial Information Theory. COSIT 2013. Lecture Notes in Computer Science, vol 8116. Springer, Cham. https://doi.org/10.1007/978-3-319-01790-7_5
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DOI: https://doi.org/10.1007/978-3-319-01790-7_5
Publisher Name: Springer, Cham
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