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. © 2006 Elsevier B.V. All rights reserved.
Kloks, T., Kratsch, D., Lee, C. M., & Liu, J. (2006). Improved bottleneck domination algorithms. Discrete Applied Mathematics, 154(11), 1578–1592. https://doi.org/10.1016/j.dam.2006.02.003