Temporal Orienteering with Changing Fuel Costs

2025-07-01

AI Summary

This paper investigates the multi-site path planning problem under time-dependent fuel costs: finding a feasible path that sequentially visits a set of target sites subject to a fuel budget constraint, where edge weights (fuel consumption) dynamically vary with both departure and arrival times—applicable to spacecraft orbital transfers. We propose a generalized temporal graph model that unifies dynamic cost functions with graph topology. We prove the problem is NP-complete and develop a polynomial-time solvable algorithmic framework parameterized by three key measures: edge usage frequency, vertex time-interval width, and number of sites to be visited. The results bridge theoretical rigor and practical relevance, establishing a novel paradigm for spatiotemporal path planning under time-varying resource constraints.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Intelligent Robots: Motion and Path Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The problem Orienteering asks whether there exists a walk which visits a number of sites without exceeding some fuel budget. In the variant of the problem we consider, the cost of each edge in the walk is dependent on the time we depart one endpoint and the time we arrive at the other endpoint. This mirrors applications such as travel between orbiting objects where fuel costs are dependent on both the departure time and the length of time spent travelling. In defining this problem, we introduce a natural generalisation of the standard notion of temporal graphs: the pair consisting of the graph of the sites and a cost function, in which costs as well as shortest travel times between pairs of objects change over time. We believe this model is likely to be of independent interest. The problem of deciding whether a stated goal is feasible is easily seen to be NP-complete; we investigate three different ways to restrict the input which lead to efficient algorithms. These include the number of times an edge can be used, an analogue of vertex-interval-membership width, and the number of sites to be visited.

Problem

• Determining feasible walks with time-dependent fuel costs
• Generalizing temporal graphs with dynamic cost functions
• Investigating restricted inputs for efficient NP-complete solutions

Innovation

• Dynamic fuel cost based on departure and arrival times
• Generalized temporal graphs with changing costs
• Efficient algorithms via edge-use and site-visit restrictions