**Area-universal rectangular layouts**.

D. Eppstein, E. Mumford, B. Speckmann, and K. Verbeek.

arXiv:0901.3924.

*25th Eur. Worksh. Comp. Geom.*, Brussels, Belgium, 2009.

*25th ACM Symp. Comp. Geom.,*Aarhus, Denmark, 2009, pp. 267–276.A partition of a rectangle into smaller rectangles is "area-universal" if any vector of areas for the smaller rectangles can be realized by a combinatorially equivalent partition. These partitions may be applied, for instance, to cartograms, stylized maps in which the shapes of countries have been distorted so that their areas represent numeric data about the countries. We characterize area-universal layouts, describe algorithms for finding them, and discuss related problems. The algorithms for constructing area-universal layouts are based on the distributive lattice structure of the set of all layouts of a given dual graph.

Merged with "Orientation-constrained rectangular layouts" to form the journal version, "Area-universal and constrained rectangular layouts".

Publications -- David Eppstein -- Theory Group -- Inf. & Comp. Sci. -- UC Irvine

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