Finding K shortest looping paths in a traffic-light network

In this paper we consider a traffic-light network where every node in the network is associated with the constraint consisting of a repeated sequence of time windows. The constraint aims to simulate the operations of traffic-light control in an intersection of roads. With this kind of constraints in place, directions of routes when passing through the intersections can be formally modeled. The objective of this paper is to find the first K shortest looping paths in the traffic-light network. An algorithm of time complexity of O(rK ²|V₁|³) is developed, where r is the number of different windows of a node and |V₁| is the number of nodes in the original network.