Maximum integer multiflow and minimum multicut problems in two-sided uniform grid graphs
In this paper, we deal with the maximum integer multiflow and the minimum multicut problems in rectilinear grid graphs with uniform capacities on the edges. The first problem is known to be NP NP -hard when any vertex can be a terminal, and we show that the second one is also NP NP -hard. Then, we study the case where the terminals are located in a two-sided way on the boundary of the outer face. We prove that, in this case, both problems are polynomial-time solvable. Furthermore, we give two efficient combinatorial algorithms using a primal-dual approach. Our work is based on previous results concerning related decision problems.
maximum integer multiflow minimum multicut grid graph