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Stick Graphs with Length Constraints

  • Steven Chaplick
  • Philipp Kindermann
  • Andre Löffler
  • Florian Thiele
  • Alexander Wolff
  • Alexander Zaft
  • Johannes ZinkEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11904)

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 (\(\textsf {STICK}_\mathsf {A}\)), and when the order of both sets is given (\(\textsf {STICK}_\mathsf {AB}\)). They showed how to solve \(\textsf {STICK}_\mathsf {AB}\) efficiently.

In this paper, we improve the running time of their algorithm, and we solve \(\textsf {STICK}_\mathsf {A}\) 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, \(\textsf {STICK}_\mathsf {A}\), and \(\textsf {STICK}_\mathsf {AB}\) are all NP-complete. On the positive side, we give an efficient solution for \(\textsf {STICK}_\mathsf {AB}\) with fixed stick lengths if there are no isolated vertices.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institut für InformatikUniversität WürzburgWürzburgGermany

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