Engineering planar separator algorithms

• Authors: Martin Holzer;Grigorios Prasinos;Frank Schulz;Dorothea Wagner;Christos Zaroliagis
• Venue: ESA'05 Proceedings of the 13th annual European conference on Algorithms
• Year: 2005

We consider classical linear-time planar separator algorithms, determining for a given planar graph a small subset of the nodes whose removal separates the graph into two components of similar size. These algorithms are based upon Planar Separator Theorems, which guarantee separators of size $O(\sqrt{n})$ and remaining components of size less than 2n/3. In this work, we present a comprehensive experimental study of the algorithms applied to a large variety of graphs, where the main goal is to find separators that do not only satisfy upper bounds but also possess other desirable qualities with respect to separator size and component balance. We propose the usage of fundamental cycles, whose size is at most twice the diameter of the graph, as planar separators: For graphs of small diameter the guaranteed bound is better than the $O(\sqrt{n})$ bounds, and it turns out that this simple strategy almost always outperforms the other algorithms, even for graphs with large diameter.