Facility Location for Congesting Commuters and Generalizing the Cost-Distance Problem

2025-11-13

AI Summary

This paper studies the congestion-aware facility location problem: how to model and solve facility location when commuters are selfish agents whose connection costs dynamically depend on path congestion. It introduces congestion effects into uncapacitated facility location for the first time, generalizing the classical Cost-Distance framework by proposing a new model based on monotonicity (non-decreasing or non-increasing) of edge cost functions. Methodologically, it integrates an approximate version of Carathéodory’s theorem with network flow modeling to design specialized approximation algorithms tailored to each monotonicity class. Key contributions include: (i) establishing the first systematic theoretical model for facility location under congestion-sensitive commuter behavior; (ii) achieving the same optimal approximation ratio as the classical Cost-Distance problem under non-increasing edge costs; and (iii) providing efficient, provably guaranteed approximation algorithms for multiple variants of the problem.

Technology Category

Constraint Satisfaction and Optimization: Distributed CSP/OptimizationSearch and Optimization: Combinatorial OptimizationPlanning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

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

Abstract

In Facility Location problems there are agents that should be connected to facilities and locations where facilities may be opened so that agents can connect to them. We depart from Uncapacitated Facility Location and by assuming that the connection costs of agents to facilities are congestion dependent, we define a novel problem, namely, Facility Location for Congesting (Selfish) Commuters. The connection costs of agents to facilities come as a result of how the agents commute to reach the facilities in an underlying network with cost functions on the edges. Inapproximability results follow from the related literature and thus approximate solutions is all we can hope for. For when the cost functions are nondecreasing we employ in a novel way an approximate version of Caratheodory's Theorem [5] to show how approximate solutions for different versions of the problem can be derived. For when the cost functions are nonincreasing we show how this problem generalizes the Cost-Distance problem [38] and provide an algorithm that for this more general case achieves the same approximation guarantees.

Problem

• Modeling congestion-dependent connection costs in facility location
• Generalizing cost-distance problems with nonincreasing cost functions
• Providing approximation algorithms for inapproximable congestion facility problems

Innovation

• Congestion-dependent connection costs for agents
• Approximate Caratheodory's Theorem for nondecreasing functions
• Generalized Cost-Distance algorithm for nonincreasing functions