Recognizing Stick Graphs with and without Length Constraints

Steven Chaplick; Philipp Kindermann; Andre Löffler; Florian Thiele; Alexander Wolff; Alexander Zaft; Johannes Zink

doi:10.7155/jgaa.00524

Recognizing Stick Graphs with and without Length Constraints

Steven Chaplick, Philipp Kindermann, Andre Löffler^*, Florian Thiele, Alexander Wolff, Alexander Zaft, Johannes Zink

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Stick graphs are intersection graphs of horizontal and vertical line segments that all touch a line of slope −1 and lie above this line. De Luca et al. [GD'18] considered the recognition problem of stick graphs when no order is given (STICK), when the order of either one of the two sets is given (STICK_A), and when the order of both sets is given (STICK_AB). They showed how to solve STICK_AB efficiently. In this paper, we improve the running time of their algorithm, and we solve STICK_A efficiently. Further, we consider variants of these problems where the lengths of the sticks are given as input. We show that these variants of STICK, STICK_A, and STICK_AB are all NP-complete. On the positive side, we give an efficient solution for STICK_AB with fixed stick lengths if there are no isolated vertices.

Original language	English
Pages (from-to)	657-681
Journal	Journal of Graph Algorithms and Applications
Volume	24
Issue number	4
DOIs	https://doi.org/10.7155/jgaa.00524
Publication status	Published - 2020

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10.7155/jgaa.00524Licence: CC BY

1 Conference article in proceeding
1 Preprint

Stick Graphs with Length Constraints
Chaplick, S., Kindermann, P., Löffler, A., Thiele, F., Wolff, A., Zaft, A. & Zink, J., 2019, Graph Drawing and Network Visualization. GD 2019. Archambault, D. & Tóth, C. (eds.). p. 3-17 15 p. (Lecture Notes in Computer Science, Vol. 11904).
Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review
Stick Graphs with Length Constraints
Chaplick, S., Kindermann, P., Löffler, A., Thiele, F., Wolff, A., Zaft, A. & Zink, J., 2019.
Research output: Working paper / Preprint › Preprint

Cite this

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title = "Recognizing Stick Graphs with and without Length Constraints",

abstract = "Stick graphs are intersection graphs of horizontal and vertical line segments that all touch a line of slope −1 and lie above this line. De Luca et al. [GD'18] considered the recognition problem of stick graphs when no order is given (STICK), when the order of either one of the two sets is given (STICKA), and when the order of both sets is given (STICKAB). They showed how to solve STICKAB efficiently. In this paper, we improve the running time of their algorithm, and we solve STICKA efficiently. Further, we consider variants of these problems where the lengths of the sticks are given as input. We show that these variants of STICK, STICKA, and STICKAB are all NP-complete. On the positive side, we give an efficient solution for STICKAB with fixed stick lengths if there are no isolated vertices.",

author = "Steven Chaplick and Philipp Kindermann and Andre L{\"o}ffler and Florian Thiele and Alexander Wolff and Alexander Zaft and Johannes Zink",

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year = "2020",

doi = "10.7155/jgaa.00524",

language = "English",

volume = "24",

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AU - Kindermann, Philipp

AU - Löffler, Andre

AU - Thiele, Florian

AU - Wolff, Alexander

AU - Zaft, Alexander

AU - Zink, Johannes

N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2020

Y1 - 2020

N2 - Stick graphs are intersection graphs of horizontal and vertical line segments that all touch a line of slope −1 and lie above this line. De Luca et al. [GD'18] considered the recognition problem of stick graphs when no order is given (STICK), when the order of either one of the two sets is given (STICKA), and when the order of both sets is given (STICKAB). They showed how to solve STICKAB efficiently. In this paper, we improve the running time of their algorithm, and we solve STICKA efficiently. Further, we consider variants of these problems where the lengths of the sticks are given as input. We show that these variants of STICK, STICKA, and STICKAB are all NP-complete. On the positive side, we give an efficient solution for STICKAB with fixed stick lengths if there are no isolated vertices.

AB - Stick graphs are intersection graphs of horizontal and vertical line segments that all touch a line of slope −1 and lie above this line. De Luca et al. [GD'18] considered the recognition problem of stick graphs when no order is given (STICK), when the order of either one of the two sets is given (STICKA), and when the order of both sets is given (STICKAB). They showed how to solve STICKAB efficiently. In this paper, we improve the running time of their algorithm, and we solve STICKA efficiently. Further, we consider variants of these problems where the lengths of the sticks are given as input. We show that these variants of STICK, STICKA, and STICKAB are all NP-complete. On the positive side, we give an efficient solution for STICKAB with fixed stick lengths if there are no isolated vertices.

U2 - 10.7155/jgaa.00524

DO - 10.7155/jgaa.00524

M3 - Article

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SP - 657

EP - 681

JO - Journal of Graph Algorithms and Applications

JF - Journal of Graph Algorithms and Applications

IS - 4

ER -

Recognizing Stick Graphs with and without Length Constraints

Abstract

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Research output

Stick Graphs with Length Constraints

Stick Graphs with Length Constraints

Cite this