Shrinking the search space for clustered planarity

Authors:
Markus Chimani;Karsten Klein
Affiliations:
Faculty of Math. and Comp. Sci., Friedrich-Schiller-University Jena, Germany;School of Information Technologies, The University of Sydney, Australia
Venue:
GD'12 Proceedings of the 20th international conference on Graph Drawing
Year:
2012

Citing 9
Cited 0

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Abstract

A clustered graph is a graph augmented with a hierarchical inclusion structure over its vertices, and arises very naturally in multiple application areas. While it is long known that planarity--i.e., drawability without edge crossings--of graphs can be tested in polynomial (linear) time, the complexity for the clustered case is still unknown. In this paper, we present a new graph theoretic reduction which allows us to considerably shrink the combinatorial search space, which is of benefit for all enumeration-type algorithms. Based thereon, we give new classes of polynomially testable graphs and a practically efficient exact planarity test for general clustered graphs based on an integer linear program.