Efficient Investment in Multi-Agent Models of Public Transportation

2026-02-03

AI Summary

This study addresses the optimization of investment strategies in public transportation systems under limited indivisible resource constraints, balancing multi-agent utility and fairness-based welfare. Focusing on two topological settings—linear routes (station selection) and weighted networks (edge traversal time optimization)—the work formulates a multi-agent resource allocation model. Theoretical analysis demonstrates that computing an approximately fair-optimal solution is NP-complete and inapproximable on general graphs. However, for a fixed number of agents—particularly in single- or two-agent scenarios—the authors propose polynomial-time algorithms combining Dijkstra’s shortest-path method with dynamic programming. These results extend to railway network design, offering both theoretical rigor and practical relevance for infrastructure planning under fairness considerations.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study two stylized, multi-agent models aimed at investing a limited, indivisible resource in public transportation. In the first model, we face the decision of which potential stops to open along a (e.g., bus) path, given agents'travel demands. While it is known that utilitarian optimal solutions can be identified in polynomial time, we find that computing approximately optimal solutions with respect to egalitarian welfare is NP-complete. This is surprising as we operate on the simple topology of a line graph. In the second model, agents navigate a more complex network modeled by a weighted graph where edge weights represent distances. We face the decision of improving travel time along a fixed number of edges. We provide a polynomial-time algorithm that combines Dijkstra's algorithm with a dynamical program to find the optimal decision for one or two agents. By contrast, if the number of agents is variable, we find \np-completeness and inapproximability results for utilitarian and egalitarian welfare. Moreover, we demonstrate implications of our results for a related model of railway network design.

Problem

• public transportation
• resource allocation
• multi-agent models
• network optimization
• computational complexity

Innovation

• multi-agent models
• egalitarian welfare
• NP-completeness
• polynomial-time algorithm
• public transportation investment