An exact approach to the problem of extracting an embedded network matrix

We study the problem of detecting a maximum embedded network submatrix in a {−1,0,+1}-matrix. Our aim is to solve the problem to optimality. We introduce a 0-1 integer linear programming formulation for this problem based on its representation over a signed graph. A polyhedral study is presented and a branch-and-cut algorithm is described for finding an optimal solution to the problem. Some computational experiments are carried out over a set of instances available in the literature as well as over a set of random instances.