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Empirical Study on Branchwidth and Branch Decomposition of Planar Graphs

We propose efficient implementations of Seymour and Thomas algorithm which, given a planar graph and an integer β, decides whether the graph has the branchwidth at least β. The computational results of our implementations show that the branchwidth of a planar graph can be computed in a practical time and memory space for some instances of size about one hundred thousand edges. Previous studies report that a straightforward implementation of the algorithm is memory consuming, which could be a bottleneck for solving instances with more than a few thousands edges. Our results suggest that with efficient implementations, the memory space required by the algorithm may not be a bottleneck in practice. Applying our implementations, an optimal branch decomposition of a planar graph of practical size can be computed in a reasonable time. Branch-decomposition based algorithms have been explored as an approach for solving many NP-hard problems on graphs. The results of this paper suggest that the approach could be practical.