Approximate solution of the maximin problem of locating facilities on a network with constraints on minimum distances

We consider the problem of the optimal location of facilities on an undirected weighted network located on a plane. The vertices are assigned positive weights and the edges are segments. The weight of a vertex reflects the requirement to locate the facilities as far away from it as possible. Constraints are given on the minimum admissible distances from vertices to the facilities. It is necessary to find such points on the edges of the network to locate the facilities that the minimum weighted distance from the vertices to the facilities is maximum. An algorithm for solving the problem with a given accuracy for two facilities is proposed.