On computing Pareto optimal paths in weighted time-dependent networks

A weighted point-availability time-dependent network is a list of temporal edges, where each temporal edge has an appearing time value, a travel time value, and a cost value. In this paper we consider the single source Pareto problem in weighted point-availability time-dependent networks, which consists of computing, for any destination , all Pareto optimal pairs , where and are the arrival time and the cost, respectively, of a path from the source to (a pair is Pareto optimal if there is no path with arrival time smaller than and cost no worse than or arrival time no greater than and better cost). We design and analyse a general algorithm for solving this problem, whose time complexity is , where is the set of temporal edges and is the maximum number of Pareto optimal pairs for each node of the network. Our algorithm can be used to solve several different minimum cost path problems in weighted point-availability time-dependent networks with a vast variety of cost definitions, and it can be easily modified in order to deal with the single destination Pareto problem. All our results apply to directed networks, but they can be easily adapted to undirected networks with no edges with zero travel time.