Monotone Simultaneous Embeddings of Paths in d Dimensions

  • David Bremner
  • Olivier Devillers
  • Marc Glisse
  • Sylvain Lazard
  • Giuseppe Liotta
  • Tamara Mchedlidze
  • Sue Whitesides
  • Stephen Wismath
Conference paper

DOI: 10.1007/978-3-319-50106-2_42

Volume 9801 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Bremner D. et al. (2016) Monotone Simultaneous Embeddings of Paths in d Dimensions. In: Hu Y., Nöllenburg M. (eds) Graph Drawing and Network Visualization. GD 2016. Lecture Notes in Computer Science, vol 9801. Springer, Cham

Abstract

We study the following problem: Given k paths that share the same vertex set, is there a simultaneous geometric embedding of these paths such that each individual drawing is monotone in some direction? We prove that, for any dimension d, there is a set of \(d+1\) paths that does not admit a monotone simultaneous geometric embedding.

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • David Bremner
    • 1
  • Olivier Devillers
    • 2
  • Marc Glisse
    • 3
  • Sylvain Lazard
    • 2
  • Giuseppe Liotta
    • 4
  • Tamara Mchedlidze
    • 5
  • Sue Whitesides
    • 6
  • Stephen Wismath
    • 7
  1. 1.University of New BrunswickFrederictonCanada
  2. 2.Inria, CNRS, University of LorraineNancyFrance
  3. 3.InriaSaclayFrance
  4. 4.University of PerugiaPerugiaItaly
  5. 5.Karlsruhe Institute of TechnologyKarlsruheGermany
  6. 6.University of VictoriaVictoriaCanada
  7. 7.University of LethbridgeLethbridgeCanada