Abstract
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 \(O(c^{\sqrt{k}}n)\) time using tree/branch-decomposition based algorithms, where c is some constant. However there has been no computational study report on the practical performances of the \(O(c^{\sqrt{k}}n)\) time 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 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 a practical time is limited to a few hundreds edges. 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.
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Marzban, M., Gu, QP., Jia, X. (2008). Computational Study on Dominating Set Problem of Planar Graphs. In: Yang, B., Du, DZ., Wang, C.A. (eds) Combinatorial Optimization and Applications. COCOA 2008. Lecture Notes in Computer Science, vol 5165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85097-7_9
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