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 journalArticleAcademicpeer-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 languageEnglish
Pages (from-to)657-681
JournalJournal of Graph Algorithms and Applications
Volume24
Issue number4
DOIs
Publication statusPublished - 2020

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  • Stick Graphs with Length Constraints

    Chaplick, S., Kindermann, P., Löffler, A., Thiele, F., Wolff, A., Zaft, A. & Zink, J., 2019.

    Research output: Working paper / PreprintPreprint

  • 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 proceedingConference article in proceedingAcademicpeer-review

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