Stick Graphs with Length Constraints

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

doi:10.1007/978-3-030-35802-0_1

Stick Graphs with Length Constraints

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

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › 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 (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.

Original language	English
Title of host publication	Graph Drawing and Network Visualization. GD 2019
Editors	D. Archambault, C. Tóth
Pages	3-17
Number of pages	15
ISBN (Electronic)	978-3-030-35802-0
DOIs	https://doi.org/10.1007/978-3-030-35802-0_1
Publication status	Published - 2019
Externally published	Yes

Publication series

Series	Lecture Notes in Computer Science
Volume	11904
ISSN	0302-9743

Keywords

INTERSECTION
INTERVAL-GRAPHS
SIZE

Access to Document

10.1007/978-3-030-35802-0_1

1 Article

Recognizing Stick Graphs with and without Length Constraints
Chaplick, S., Kindermann, P., Löffler, A., Thiele, F., Wolff, A., Zaft, A. & Zink, J., 2020, In: Journal of Graph Algorithms and Applications. 24, 4, p. 657-681
Research output: Contribution to journal › Article › Academic › peer-review

Open Access

Cite this

@inproceedings{aef9bf7191454de499380c5b206949db,

title = "Stick Graphs with 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.",

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

note = "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.",

year = "2019",

doi = "10.1007/978-3-030-35802-0_1",

language = "English",

isbn = "978-3-030-35801-3",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "3--17",

editor = "D. Archambault and C. T{\'o}th",

booktitle = "Graph Drawing and Network Visualization. GD 2019",

}

Stick Graphs with Length Constraints. / Chaplick, Steven; Kindermann, Philipp; Löffler, Andre et al.
Graph Drawing and Network Visualization. GD 2019. ed. / D. Archambault; C. Tóth. 2019. p. 3-17 (Lecture Notes in Computer Science, Vol. 11904).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

TY - GEN

T1 - Stick Graphs with Length Constraints

AU - Chaplick, Steven

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 - 2019

Y1 - 2019

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.

KW - INTERSECTION

KW - INTERVAL-GRAPHS

KW - SIZE

U2 - 10.1007/978-3-030-35802-0_1

DO - 10.1007/978-3-030-35802-0_1

M3 - Conference article in proceeding

SN - 978-3-030-35801-3

T3 - Lecture Notes in Computer Science

SP - 3

EP - 17

BT - Graph Drawing and Network Visualization. GD 2019

A2 - Archambault, D.

A2 - Tóth, C.

ER -

Stick Graphs with Length Constraints

Abstract

Publication series

Keywords

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Research output

Recognizing Stick Graphs with and without Length Constraints

Cite this