The Model and Properties of the Traffic Light Problem

Abstract

The traffic network of a city can be modeled by a graph in which vertices represent the intersections of roads and edges represent the segments of roads. The traffic light problem is concerned with the setting of the starting time of the green light for each traffic light such that the total waiting time of the traffic in the traffic network is minimized. In this paper, we first prove that the traffic light problem is NP-hard for the traffic The traffic network of a city can be modeled by a graph in which vertices represent the intersections of roads and edges represent the segments of roads. The traffic light problem is concerned with the setting of the starting time of the green light for each traffic light such that the total waiting time of the traffic in the traffic network is minimized. In this paper, we first prove that the traffic light problem is NP-hard for the traffic light cycle T≧3, that the traffic light problem on a planar graph with T=2 can be solved by the algorithm designed for the weighted maximum cut problem, whose time complexity is O(n3/2 log n), and that the two phase setting problem ( a special case of the traffic light problem) on a planar graph can also be solved in the same time complexity. Then , we discuss some properties of the traffic light problem to find the minimum penalty of a polygon with n edges in O(n) time. Finally, we present a heuristic algorithm to solve the traffic light problem and show some experiment results.