Optimizing regular edge labelings

Authors:
Kevin Buchin;Bettina Speckmann;Sander Verdonschot
Affiliations:
Dep. of Mathematics and Computer Science, TU Eindhoven, The Netherlands;Dep. of Mathematics and Computer Science, TU Eindhoven, The Netherlands;School of Computer Science, Carleton University, Canada
Venue:
GD'10 Proceedings of the 18th international conference on Graph drawing
Year:
2010

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Abstract

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.