Computing Maximum C-planar Subgraphs
Chimani, Markus and Gutwenger, Carsten and Jansen, Mathias and Klein, Karsten and Mutzel, Petra (2009) Computing Maximum C-planar Subgraphs. In: Graph Drawing 16th International Symposium, GD 2008, September 21- 24, 2008, Heraklion, Crete, Greece , pp. 115-120 (Official URL: http://dx.doi.org/10.1007/978-3-642-00219-9_12).
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Deciding c-planarity for a given clustered graph C = (G, T ) is one of the most challenging problems in current graph drawing research. Though it is yet unknown if this problem is solvable in polynomial time, latest research focused on algorithmic approaches for special classes of clustered graphs. In this paper, we introduce an approach to solve the general problem using integer linear programming (ILP) techniques. We give an ILP formulation that also includes the natural generalization of cplanarity testing—the maximum c-planar subgraph problem —and solve this ILP with a branch-and-cut algorithm. Our computational results show that this approach is already successful for many clustered graphs of small to medium sizes and thus can be the foundation of a practically eﬃcient algorithm that integrates further sophisticated ILP techniques.
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