Total Positive Influence Domination on Weighted Networks.

We are proposing two greedy and a new linear programming based approximation algorithm for the total positive influence dominating set problem in weighted networks. Applications of this problem in weighted settings include finding: a minimum cost set of nodes to broadcast a message in social networks, such that each node has majority of neighbours broadcasting that message; a maximum trusted set in bit-coin network; an optimal set of hosts when running distributed apps etc.. Extensive experiments on different generated and real networks highlight advantages and potential issues for each algorithm.