Exact and heuristic algorithms for the weighted total domination problem

Dominating set problems are among the most important class of combinatorial in graph optimization, from a theoretical as well practical point view. In this paper, we address recently introduced (minimum) weighted total domination problem. problem, given an undirected with vertex weight function and edge function. The goal is to find dominating D minimal weight. A subset vertices such that every graph, including D, adjacent D. measured by sum all weights edges subgraph induced plus for each not minimum outside present two new Mixed-Integer Programming models design solution frameworks based on them. These also include valid inequalities, starting heuristics primal heuristics. addition, develop genetic algorithm, which greedy randomized adaptive search procedure version our heuristic. We carry out computational study assess performance approaches when compared previous work same reveals exact algorithms up 500 times faster instances 125 can be solved optimality within timelimit 1800 s. Moreover, presented algorithm works often finds optimal or near-optimal short runtime. Additionally, analyze influence instance-characteristics algorithms.