@article{c7c01fe4b1f745c98c7489d7de41422c,
title = "Simple algorithms for partial and simultaneous rectangular duals with given contact orientations",
abstract = "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. The simultaneous representation problem for rectangular duals asks whether two (or more) given graphs that share a subgraph admit rectangular duals that coincide on the shared subgraph. Combinatorially, a rectangular dual can be described by a regular edge labeling (REL), which determines the orientations of the rectangle contacts.We describe linear-time algorithms for the partial representation extension problem and the simultaneous representation problem for rectangular duals when each input graph is given together with a REL. Both algorithms are based on formulations as linear programs, yet they have geometric interpretations and can be seen as extensions of the classic algorithm by Kant and He that computes a rectangular dual for a given graph. (C) 2022 Elsevier B.V. All rights reserved.",
keywords = "EXTENDING PARTIAL REPRESENTATIONS, Partial representation extension, Rectangular dual, Simultaneous representation",
author = "Steven Chaplick and Stefan Felsner and Philipp Kindermann and Jonathan Klawitter and Ignaz Rutter and Alexander Wolff",
note = "Funding Information: Partially supported by DFG grants Ru 1903/3-1 and Wo 758/11-1 . We thank the anonymous reviewers for their helpful comments. Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",
year = "2022",
month = jun,
day = "5",
doi = "10.1016/j.tcs.2022.03.031",
language = "English",
volume = "919",
pages = "66--74",
journal = "Theoretical Computer Science",
issn = "0304-3975",
publisher = "Elsevier Science",
}