International Symposium on Graph Drawing

GD 2007: Graph Drawing pp 159-170

Efficient Extraction of Multiple Kuratowski Subdivisions

  • Markus Chimani
  • Petra Mutzel
  • Jens M. Schmidt
Conference paper

DOI: 10.1007/978-3-540-77537-9_17

Volume 4875 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Chimani M., Mutzel P., Schmidt J.M. (2008) Efficient Extraction of Multiple Kuratowski Subdivisions. In: Hong SH., Nishizeki T., Quan W. (eds) Graph Drawing. GD 2007. Lecture Notes in Computer Science, vol 4875. Springer, Berlin, Heidelberg

Abstract

A graph is planar if and only if it does not contain a Kuratowski subdivision. Hence such a subdivision can be used as a witness for non-planarity. Modern planarity testing algorithms allow to extract a single such witness in linear time. We present the first linear time algorithm which is able to extract multiple Kuratowski subdivisions at once. This is of particular interest for, e.g., Branch-and-Cut algorithms which require multiple such subdivisions to generate cut constraints. The algorithm is not only described theoretically, but we also present an experimental study of its implementation.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Markus Chimani
    • 1
  • Petra Mutzel
    • 1
  • Jens M. Schmidt
    • 1
  1. 1.Department of Computer ScienceUniversity of DortmundGermany