Proportional Contact Representations of Planar Graphs
نویسندگان
چکیده
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. Submitted: November 2011 Reviewed: April 2012 Revised: May 2012 Reviewed: July 2012 Revised: August 2012 Accepted: August 2012 Final: September 2012 Published: September 2012 Article type: Regular paper Communicated by: M. van Kreveld and B. Speckmann Research funded in part by EUROGIGA project GraDR, DFG Fe 340/7-2NSF, NSERC, and NSF grants CCF-0545743 and CCF-1115971. E-mail addresses: [email protected] (Md. Jawaherul Alam) [email protected] (Therese Biedl) [email protected] (Stefan Felsner) [email protected] (Michael Kaufmann) [email protected] (Stephen G. Kobourov) 702 Alam et al. Proportional Contact Representations of Planar Graphs
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Proportional Contact Representations of Planar Graphs Technical Report CS 2011 - 11
We study contact representations for planar graphs, with vertices represented by simple polygons and adjacencies represented by a point-contact or a side-contact between the corresponding polygons. Specifically, we consider proportional contact representations, where given vertex weights are represented by the areas of the corresponding polygons. Several natural optimization goals for such repr...
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