math - Dominating Set Greedy Approximation Worst-Case Example -


to find minimum dominating set of undirected graph g can use greedy algorithm this: start empty set d. until d dominating set, add vertex v maximum number of uncovered neighbours.

the algorithm not find optimal solution, ln(delta)-approximation. (if delta maximum degree of vertex in g)

now looking simple example greedy algorithm not find optimal solution. 1 found related instance of set cover problem. (http://en.wikipedia.org/wiki/set_cover_problem#greedy_algorithm picture on right) translating 1 graph cause minimum of 14 vertices , lot of edges.

does know small example?

thanks in advance

consider following graph:

enter image description here

a greedy approach choose b d , g. meanwhile, e , f form dominating set.


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