Extending Partial Representations of Rectangular Duals with Given Contact Orientations

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

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic


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.keywordsrectangular dualpartial representation extension.
Original languageEnglish
Title of host publicationAlgorithms and Complexity
Subtitle of host publication12th International Conference, CIAC 2021, Virtual Event, May 10–12, 2021, Proceedings
EditorsTiziana Calamoneri, Federico Coro
PublisherSpringer Nature
ISBN (Print)978-3-030-75241-5
Publication statusPublished - 2021
Event12th International Conference on Algorithms and Complexity - Online, University of Cyprus, Cyprus
Duration: 10 May 202112 May 2021
Conference number: 12

Publication series

SeriesLecture Notes in Computer Science


Conference12th International Conference on Algorithms and Complexity
Abbreviated titleCIAC 2021
Internet address


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