Extending Partial Representations of Rectangular Duals with Given Contact Orientations

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

doi:10.48550/arXiv.2102.02013

Extending Partial Representations of Rectangular Duals with Given Contact Orientations

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

Research output: Working paper / Preprint › Preprint

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.

Original language	English
Number of pages	14
Volume	abs/2102.02013
DOIs	https://doi.org/10.48550/arXiv.2102.02013
Publication status	Published - Feb 2021

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10.48550/arXiv.2102.02013

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., 2021, Algorithms and Complexity: 12th International Conference, CIAC 2021, Virtual Event, May 10–12, 2021, Proceedings. Calamoneri, T. & Corò, F. (eds.). Springer Nature, p. 340-353 14 p. (Lecture Notes in Computer Science, Vol. 12701).
Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

Cite this

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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.",

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N2 - 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.

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.

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M3 - Preprint

VL - abs/2102.02013

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

ER -

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