Monge matrices make maximization manageable

The authors continue the research on the effects of Monge structures in the area of combinatorial optimization. They show that three optimization problems become easy if the underlying cost matrix fulfills the Monge property: (A) The Balanced max-cut problem, (B) the problem of computing minimum weight binary k-matchings and (C) the computation of longest paths in bipartite, edge-weighted graphs. In all three results, the authors first prove that the Monge structure imposes some special combinatorial property on the structure of the optimum solution. and then they exploit this combinatorial property to derive efficient algorithms.