Extending Partial Representations of Rectangular Duals with Given Contact Orientations

Steven Chaplick, Philipp Kindermann, Jonathan Klawitter, Ignaz Rutter, Alexander Wolff

Research output: Working paper / PreprintPreprint


A rectangular dual of a graph G is a contact representation of G by axis-aligned rectangles such that (i) no four rectangles share a point and (ii) the union of all rectangles is a rectangle. The partial representation extension problem for rectangular duals asks whether a given partial rectangular dual can be extended to a rectangular dual, that is, whether there exists a rectangular dual where some vertices are represented by prescribed rectangles. Combinatorially, a rectangular dual can be described by a regular edge labeling (REL), which determines the orientations of the rectangle contacts. We characterize the RELs that admit an extension, which leads to a linear-time testing algorithm. In the affirmative, we can construct an extension in linear time.
Original languageEnglish
Number of pages14
Publication statusPublished - Feb 2021

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