Min-max model for the network reduction problem

We deal with solving a NP-hard problem that occurs in reduction of transport networks. The reduction means to omit some edges. There are two requirements imposed on the resulting reduced network: First, the upper bound of the total length of reduced network is known. Second, the distance between arbitrary two points in reduced network should not exceed q-multiple of that in original network, where q should be as small as possible. There are many applications of just mentioned problem e.g. when designing a bus line system in a town. We present a constraint programming formulation and an exact solution using MiniZinc model.