Geodesic
Overlapping Cluster Planarity
Journal of Graph Algorithms and Applications, Special Issue on Selected Papers from the 6th Asia-Pacific Symposium on Visualisation, APVIS 2007 , Tome 12 (2008) no. 3, pp. 267-291.

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This paper investigates a new direction in the area of cluster planarity by addressing the following question: Let G be a graph along with a hierarchy of vertex clusters, where clusters can partially intersect. Does G admit a drawing where each cluster is inside a simple closed region, no two edges intersect, and no edge intersects a region twice? We investigate the interplay between this problem and the classical cluster planarity testing problem where clusters are not allowed to partially intersect. Characterizations, models, and algorithms are discussed. 
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     author = {Walter Didimo and Francesco Giordano and Giuseppe Liotta},
     title = {Overlapping {Cluster} {Planarity}},
     journal = {Journal of Graph Algorithms and Applications},
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     doi = {10.7155/jgaa.00167},
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     url = {http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00167/}
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Walter Didimo; Francesco Giordano; Giuseppe Liotta. Overlapping Cluster Planarity. Journal of Graph Algorithms and Applications, 
							Special Issue on Selected Papers from the 6th Asia-Pacific Symposium on Visualisation, APVIS 2007
					, Tome 12 (2008) no. 3, pp. 267-291. doi : 10.7155/jgaa.00167. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00167/

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