Computational Study on Dominating Set Problem of Planar Graphs

  • Authors:

  • Marjan Marzban;Qian-Ping Gu;Xiaohua Jia

  • Affiliations:

  • School of Computing Science, Simon Fraser University, Burnaby BC, Canada;School of Computing Science, Simon Fraser University, Burnaby BC, Canada;Department of Computer Science, City University of Hong Kong,

  • Venue:
  • COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
  • Year:
  • 2008

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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 nvertices and dominating number kcan be solved in $O(c^{\sqrt{k}}n)$ time using tree/branch-decomposition based algorithms, where cis 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.