Extending Partial Representations of Rectangular Duals with Given Contact Orientations

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

doi:10.1007/978-3-030-75242-2_24

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 proceeding › Chapter › Academic

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. 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 language	English
Title of host publication	Algorithms and Complexity
Subtitle of host publication	12th International Conference, CIAC 2021, Virtual Event, May 10–12, 2021, Proceedings
Editors	Tiziana Calamoneri, Federico Coro
Publisher	Springer Nature
Pages	340-353
ISBN (Print)	978-3-030-75241-5
DOIs	https://doi.org/10.1007/978-3-030-75242-2_24
Publication status	Published - 2021
Event	12th International Conference on Algorithms and Complexity - Online, University of Cyprus, Cyprus Duration: 10 May 2021 → 12 May 2021 Conference number: 12 http://easyconferences.eu/ciac2021/

Publication series

Series	Lecture Notes in Computer Science
Volume	12701
ISSN	0302-9743

Conference

Conference	12th International Conference on Algorithms and Complexity
Abbreviated title	CIAC 2021
Country/Territory	Cyprus
Period	10/05/21 → 12/05/21
Internet address	http://easyconferences.eu/ciac2021/

Access to Document

10.1007/978-3-030-75242-2_24

1 Article
1 Preprint

Simple algorithms for partial and simultaneous rectangular duals with given contact orientations
Chaplick, S., Felsner, S., Kindermann, P., Klawitter, J., Rutter, I. & Wolff, A., 5 Jun 2022, In: Theoretical Computer Science. 919, p. 66-74 9 p.
Research output: Contribution to journal › Article › Academic › peer-review
Extending Partial Representations of Rectangular Duals with Given Contact Orientations
Chaplick, S., Kindermann, P., Klawitter, J., Rutter, I. & Wolff, A., Feb 2021, 14 p.
Research output: Working paper / Preprint › Preprint

Cite this

Chaplick, S., Kindermann, P., Klawitter, J., Rutter, I., & Wolff, A. (2021). Extending Partial Representations of Rectangular Duals with Given Contact Orientations. In T. Calamoneri, & F. Coro (Eds.), Algorithms and Complexity: 12th International Conference, CIAC 2021, Virtual Event, May 10–12, 2021, Proceedings (pp. 340-353). Springer Nature. https://doi.org/10.1007/978-3-030-75242-2_24

Chaplick, Steven ; Kindermann, Philipp ; Klawitter, Jonathan et al. / Extending Partial Representations of Rectangular Duals with Given Contact Orientations. Algorithms and Complexity: 12th International Conference, CIAC 2021, Virtual Event, May 10–12, 2021, Proceedings. editor / Tiziana Calamoneri ; Federico Coro. Springer Nature, 2021. pp. 340-353 (Lecture Notes in Computer Science, Vol. 12701).

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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. 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.",

author = "Steven Chaplick and Philipp Kindermann and Jonathan Klawitter and Ignaz Rutter and Alexander Wolff",

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Chaplick, S, Kindermann, P, Klawitter, J, Rutter, I & Wolff, A 2021, Extending Partial Representations of Rectangular Duals with Given Contact Orientations. in T Calamoneri & F Coro (eds), Algorithms and Complexity: 12th International Conference, CIAC 2021, Virtual Event, May 10–12, 2021, Proceedings. Springer Nature, Lecture Notes in Computer Science, vol. 12701, pp. 340-353, 12th International Conference on Algorithms and Complexity, Cyprus, 10/05/21. https://doi.org/10.1007/978-3-030-75242-2_24

Extending Partial Representations of Rectangular Duals with Given Contact Orientations. / Chaplick, Steven; Kindermann, Philipp; Klawitter, Jonathan et al.
Algorithms and Complexity: 12th International Conference, CIAC 2021, Virtual Event, May 10–12, 2021, Proceedings. ed. / Tiziana Calamoneri; Federico Coro. Springer Nature, 2021. p. 340-353 (Lecture Notes in Computer Science, Vol. 12701).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

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T1 - Extending Partial Representations of Rectangular Duals with Given Contact Orientations

AU - Chaplick, Steven

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AB - 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.

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Chaplick S, Kindermann P, Klawitter J, Rutter I, Wolff A. Extending Partial Representations of Rectangular Duals with Given Contact Orientations. In Calamoneri T, Coro F, editors, Algorithms and Complexity: 12th International Conference, CIAC 2021, Virtual Event, May 10–12, 2021, Proceedings. Springer Nature. 2021. p. 340-353. (Lecture Notes in Computer Science, Vol. 12701). doi: 10.1007/978-3-030-75242-2_24

Extending Partial Representations of Rectangular Duals with Given Contact Orientations

Abstract

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Research output

Simple algorithms for partial and simultaneous rectangular duals with given contact orientations

Extending Partial Representations of Rectangular Duals with Given Contact Orientations

Cite this