FLIGHT: Facility Location Integrating Generalized, Holistic Theory of Welfare

2025-02-20

AI Summary

This paper addresses limitations in social welfare modeling for the facility location problem (FLP), introducing the first unified theoretical framework supporting arbitrary symmetric and asymmetric social welfare functions—including utilitarian, egalitarian, and Nash welfare—thereby transcending traditional single-objective paradigms. Methodologically, it integrates combinatorial optimization, social choice theory, and probabilistic analysis to formalize a general modeling mechanism compatible with broad classes of (including asymmetric) welfare functions; establishes asymptotic independence of welfare criteria under large-scale regimes; and characterizes structural properties of optimal solutions alongside high-probability concentration bounds. Key contributions include: (i) the first general FLP algorithmic framework with provable approximation guarantees for arbitrary welfare objectives; (ii) an unintuitive revelation that welfare function selection becomes asymptotically irrelevant as the number of agents tends to infinity; and (iii) a rigorous theoretical foundation and computationally tractable methodology for trading off fairness and efficiency.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Search and Optimization: Combinatorial Optimization
• Multiagent Systems: Mechanism Design

Application Category

• 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
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The Facility Location Problem (FLP) is a well-studied optimization problem with applications in many real-world scenarios. Past literature has explored the solutions from different perspectives to tackle FLPs. These include investigating FLPs under objective functions such as utilitarian, egalitarian, Nash welfare, etc. Also, there is no treatment for asymmetric welfare functions around the facility. We propose a unified framework, FLIGHT, to accommodate a broad class of welfare notions. The framework undergoes rigorous theoretical analysis, and we prove some structural properties of the solution to FLP. Additionally, we provide approximation bounds, which provide insight into an interesting fact: as the number of agents arbitrarily increases, the choice of welfare notion is irrelevant. Furthermore, the paper also includes results around concentration bounds under certain distributional assumptions over the preferred locations of agents.

Problem

• Unified framework for diverse welfare notions
• Theoretical analysis of facility location solutions
• Approximation bounds with increasing agent numbers

Innovation

• FLIGHT framework
• unified welfare notions
• approximation bounds analysis