Beyond Level Planarity

  • Patrizio Angelini
  • Giordano Da Lozzo
  • Giuseppe Di Battista
  • Fabrizio Frati
  • Maurizio Patrignani
  • Ignaz Rutter
Conference paper

DOI: 10.1007/978-3-319-50106-2_37

Volume 9801 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Angelini P., Da Lozzo G., Di Battista G., Frati F., Patrignani M., Rutter I. (2016) Beyond Level Planarity. In: Hu Y., Nöllenburg M. (eds) Graph Drawing and Network Visualization. GD 2016. Lecture Notes in Computer Science, vol 9801. Springer, Cham

Abstract

In this paper we settle the computational complexity of two open problems related to the extension of the notion of level planarity to surfaces different from the plane. Namely, we show that the problems of testing the existence of a level embedding of a level graph on the surface of the rolling cylinder or on the surface of the torus, respectively known by the name of Cyclic Level Planarity and Torus Level Planarity, are polynomial-time solvable.

Moreover, we show a complexity dichotomy for testing the Simultaneous Level Planarity of a set of level graphs, with respect to both the number of level graphs and the number of levels.

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Giordano Da Lozzo
    • 2
  • Giuseppe Di Battista
    • 2
  • Fabrizio Frati
    • 2
  • Maurizio Patrignani
    • 2
  • Ignaz Rutter
    • 3
  1. 1.Tübingen UniversityTübingenGermany
  2. 2.Roma Tre UniversityRomeItaly
  3. 3.Karlsruhe Institute of TechnologyKarlsruheGermany