Algorithms for Shortest Path Tour Problem in Large-Scale Road Network

Yucen Gao, Mingqian Ma, Jiale Zhang, Songjian Zhang, Jun Fang, Xiaofeng Gao, Guihai Chen

Abstract: Carpooling route planning becomes an important problem with the growth of low-carbon traffic systems. When each passenger has several potential locations to get on and off the car, the problem will be more challenging. In the paper, we discussed a simplified carpooling route planning problem, namely the Shortest Path Tour Problem (SPTP), whose aim is to find a single-origin single-destination shortest path through an ordered sequence of disjoint node subsets. We propose Stage Dijkstra and Global Dijkstra algorithms to find the optimal shortest path, with the time complexity of \(O(l(n+m)\log n)\) and \(O(l(n+m)\log (ln))\) respectively, where l represents the number of node subsets. To the best of our knowledge, \(O(l(n+m)\log n)\) is the best time complexity of the exact algorithms for SPTP. Experiments conducted on large-scale road networks and synthetic datasets demonstrate the effectiveness and efficiency of our proposed algorithms.