Modular Circulation and Applications to Traffic Management

摘要

We introduce a variant of the well-known minimum-cost circulation problem in directed networks, where vertex demand values are taken from the integers modulo lambda, for some integer lambda >= 2. More formally, given a directed network G = (V, E), each of whose edges is associated with a weight and each of whose vertices is associated with a demand taken over the integers modulo lambda, the objective is to compute a flow of minimum weight that satisfies all the vertex demands modulo lambda. This problem is motivated by a problem of computing a periodic schedule for traffic lights in an urban transportation network that minimizes the total delay time of vehicles. We show that this modular circulation problem is solvable in polynomial time when lambda = 2 and that the problem is NP-hard when lambda = 3. We also present a polynomial time algorithm that achieves a 4(lambda - 1)-approximation.