A mathematical programming approach for recognizing binet matrices

The development of an efficient and practical method to recognize matrices originating from generalized graphs, in the same way that network matrices are defined over directed graphs, remains an open question. In this paper we present such a recognition procedure for binet matrices which are known to characterize an important class of integral polyhedra. A mathematical programming formulation for the recognition problem is provided, where the special structure of these matrices is expressed via a set of constraints. Finally, given that binet matrices represent certain classes of matroids, we present a set of areas ranging from combinatorial optimization to matroid theory that can benefit from our approach.