Optimizing Regular Edge Labelings
Buchin, Kevin and Speckmann, Bettina and Verdonschot, Sander (2011) Optimizing Regular Edge Labelings. In: Graph Drawing 18th International Symposium, GD 2010, September 21-24, 2010, Konstanz, Germany , pp. 117-128 (Official URL: http://dx.doi.org/10.1007/978-3-642-18469-7_11).
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A regular edge labeling (REL) of an irreducible triangulation G uniquely defines a rectangular dual of G. Rectangular duals find applications in various areas: as floor plans of electronic chips, in architectural designs, as rectangular cartograms, or as treemaps. An irreducible triangulation can have many RELs and hence many rectangular duals. Depending on the specific application different duals might be desirable. In this paper we consider optimization problems on RELs and show how to find optimal or near-optimal RELs for various quality criteria. Furthermore, we give upper and lower bounds on the number of RELs.
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