Computational Study on Dominating Set Problem of Planar Graphs

Abstract: Recently, there have been significant theoretical progresses towards fixed-parameter algorithms for the DOMINATING SET problem of planar graphs. It is known that the problem of a planar graph with n vertices and dominating number k can be solved in O(c k n) time, where c is some constant. However there has been no computational study report on the practical performances of the O(c k n) time algorithms. In this paper, we report the computational results of Fomin and Thilikos algorithm which uses the branch-decomposition based approach and achieves the smallest constant c = 215.13 among these algorithms. 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 algo...

• Type: Conference
• Year: 2008
• Where: COCOA
• Authors: Marjan Marzban, Qian-Ping Gu, Xiaohua Jia
• Keywords: Algorithm, COCOA 2008, Discrete Geometry, Dominating Set Problem, Planar Graphs