Geodesic
Fitting Planar Graphs on Planar Maps
Journal of Graph Algorithms and Applications, Tome 19 (2015) no. 1, pp. 413-440.

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Graph and cartographic visualization have the common objective to provide intuitive understanding of some underlying data. We consider a problem that combines aspects of both by studying the problem of fitting planar graphs on planar maps. After providing an NP-hardness result for the general decision problem, we identify sufficient conditions so that a fit is possible on a map with rectangular regions. We generalize our techniques to non-convex rectilinear polygons, where we also address the problem of efficient distribution of the vertices inside the map regions.
DOI : 10.7155/jgaa.00367
Keywords: cluster planarity, rectangle contact maps, rectilinear contact maps, NP-Hard, Shortest Path 
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Md. Jawaherul Alam; Michael Kaufmann; Stephen Kobourov; Tamara Mchedlidze. Fitting Planar Graphs on Planar Maps. Journal of Graph Algorithms and Applications, Tome 19 (2015) no. 1, pp. 413-440. doi : 10.7155/jgaa.00367. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00367/

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