Computational study on planar dominating set problem

Recently, there has been significant theoretical progress towards fixed-parameter algorithms for the DOMINATING SET problem of planar graphs. It is known that the problem on a planar graph with n vertices and dominating number k can be solved in time using tree/branch-decomposition based algorithms. In this paper, we report computational results of Fomin and Thilikos algorithm which uses the branch-decomposition based approach. The computational results show that the algorithm can solve the DOMINATING SET problem of large planar graphs in a practical time and memory space for the class of graphs with small branchwidth. For the class of graphs with large branchwidth, the size of instances that can be solved by the algorithm in practice is limited to about one thousand edges due to a memory space bottleneck. The practical performances of the algorithm coincide with the theoretical analysis of the algorithm. The results of this paper suggest that the branch-decomposition based algorithms can be practical for some applications on planar graphs.