The Generalized Max-Controlled Set Problem

In this work we deal with sandwich graphs G = ( V , E ) and present the notion of vertices f-controlled by a subset M ⊆ V . We introduce the generalized max-controlled set problem (gmcsp), where gaps and positive weights are associated to each vertex of V. In this case, the objective is find a sandwich graph G in order to maximize the sum of the weights associated to all vertices f-controlled by M. We present a 1 2 -approximation algorithm for the gmcsp and a new procedure for finding feasible solutions based on a linear relaxation. The best solution is then used as starting point in a local search procedure (Tabu Search with Path Relinking). Finally, we present some computational results and compare the performance of our heuristics with the optimum solution value of some instances of the problem.