Finding the K shortest paths in a schedule-based transit network

Finding the shortest paths in a schedule-based public transit network is similar to finding the shortest paths in a network with multi-costs constrained and time-window constraints. We consider a schedule-based transit network, where each node in the network has a list of scheduled departure times for transit vehicles. The objective of this paper is to find out the first K   shortest paths in a schedule-based transit network. An algorithm with a time complexity of O(S¯2L¯3)+O(L¯4S¯Rlmax)+O(S¯L¯RlmaxK(L¯3log(L¯3)+L¯3)) is proposed to enumerate these paths. We compare the time complexity of our algorithm with that of two existing path finding algorithms. We show that our algorithm has a better performance in computational time complexity than the two existing path finding algorithms, though it is only applicable if the number of transfers does not exceed 2. Also, for large sized real transit network, our algorithm determines the K shortest paths in a much shorter time frame than the existing two algorithms.