On Computing Pareto Optimal Paths in Weighted Time-Dependent Networks

TL;DR

This paper introduces an efficient algorithm for computing all Pareto optimal paths in weighted point-availability time-dependent networks, significantly improving previous solutions and applicable to various cost definitions.

Contribution

The authors present a novel algorithm with a complexity of O(M log P) for the single source Pareto problem in weighted time-dependent networks, enhancing efficiency over prior methods.

Findings

Algorithm achieves O(M log P) complexity

Applicable to diverse cost functions in time-dependent networks

Can be adapted for undirected networks without zero travel time edges

Abstract

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 d, all Pareto optimal pairs (t, c), where t and c are the arrival time and the cost of a path from s to d, respectively (a pair (t, c) is Pareto optimal if there is no path with arrival time smaller than t and cost no worse than c or arrival time no greater than t and better cost). We design and analyse a general algorithm for solving this problem, whose time complexity is O(M log P), where M is the number of temporal edges and P is the maximum number of Pareto optimal pairs for each node of the network. This complexity significantly improves the time complexity of the previously known solution. 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.