Improved bottleneck domination algorithms

Authors:
Ton Kloks;Dieter Kratsch;Chuan-Min Lee;Jiping Liu
Affiliations:
Department of Mathematics and Computer Science, The University of Lethbridge, Alta, Canada;Université de Metz, LITA, Metz, Cedex, France;Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi, Taiwan;Department of Mathematics and Computer Science, The University of Lethbridge, Alta, Canada
Venue:
Discrete Applied Mathematics
Year:
2006

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Abstract

W.C.K. Yen introduced BOTTLENECK DOMINATION and BOTTLENECK INDEPENDENT DOMINATION. He presented an O(n log n + m)- time algorithm to compute a minimum bottleneck dominating set. He also obtained that the BOTTLENECK INDEPENDENT DOMINATING SET problem is NP-complete, even when restricted to planar graphs.We present simple linear time algorithms for the BOTTLENECK DOMINATING SET and the BOTTLENECK TOTAL DOMINATING SET problem. Furthermore, we give polynomial time algorithms (most of them with linear time-complexities) for the BOTTLENECK INDEPENDENT DOMINATING SET problem on the following graph classes: AT-free graphs, chordal graphs, split graphs, permutation graphs, graphs of bounded treewidth, and graphs of clique-width at most k with a given k-expression.