Geodesic
Proportional Contact Representations of Planar Graphs
Journal of Graph Algorithms and Applications, Special Issue on Selected Papers from the Nineteenth International Symposium on Graph Drawing, GD 2011 , Tome 16 (2012) no. 3, pp. 701-728.

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We study contact representations for planar graphs, with vertices represented by simple polygons and adjacencies represented by point-contacts or side-contacts between the corresponding polygons. Specifically, we consider proportional contact representations, where pre-specified vertex weights must be represented by the areas of the corresponding polygons. Natural optimization goals for such representations include minimizing the complexity of the polygons, and the unused area. We describe algorithms for proportional contact representations with optimal polygonal complexity for general planar graphs and planar 2-segment graphs, which include maximal outer-planar graphs and partial 2-trees. 
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     author = {Md. Jawaherul Alam and Therese Biedl and Stefan Felsner and Michael Kaufmann and Stephen Kobourov},
     title = {Proportional {Contact} {Representations} of {Planar} {Graphs}},
     journal = {Journal of Graph Algorithms and Applications},
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     doi = {10.7155/jgaa.00276},
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     url = {http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00276/}
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Md. Jawaherul Alam; Therese Biedl; Stefan Felsner; Michael Kaufmann; Stephen Kobourov. Proportional Contact Representations of Planar Graphs. Journal of Graph Algorithms and Applications, 
							Special Issue on Selected Papers from the Nineteenth International Symposium on Graph Drawing, GD 2011
					, Tome 16 (2012) no. 3, pp. 701-728. doi : 10.7155/jgaa.00276. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00276/

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