Efficient extraction of multiple kuratowski subdivisions

Authors:
Markus Chimani;Petra Mutzel;Jens M. Schmidt
Affiliations:
Department of Computer Science, University of Dortmund, Germany;Department of Computer Science, University of Dortmund, Germany;Department of Computer Science, University of Dortmund, Germany
Venue:
GD'07 Proceedings of the 15th international conference on Graph drawing
Year:
2007

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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.