We study the minimum weighted dominating set problem in graphs. We give polynomial algorithms for cacti, and the first polynomial combinatorial algorithm for cycles. The previously known polynomial algorithm for cycles is based on the ellipsoid method. We also show that by adding extra variables, this can be formulated as a linear program of polynomial size.
Additionally we study the p-dominating set problem, where the cardinality of the set is required to be exactly p. We show that the natural linear programming formulation gives an integral polytope when the graph is a cycle. We also give a polynomial combinatorial algorithm for cacti.
By: Mourad Baïou, Francisco Barahona
Published in: RC25488 in 2014
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