Year: 2026
Type: preprint
Abstract: In spatial matching markets, a supply unit's flexibility is measured by its service radius, the maximum distance at which it can serve demand. In dimensions $k \geq 2$, we study how a platform should allocate service radii among the supply nodes subject to a budget on their sum. The platform makes this choice before observing supply and demand locations, with the objective of maximizing the expected fulfilled demand. We show that the shape of a preferred allocation depends on the total budget: under suitable conditions, large budgets favor allocations that are more uniform in the sense of majorization, while small budgets favor concentration. We also characterize a non-uniform allocation that is asymptotically optimal for a very-sparse regime, and show that the uniform allocation is suboptimal in this regime. Our results provide theoretical explanations for the radius allocation questions raised by the numerical experiments in [ASY26b].
Source: arXiv (Cornell University)
Authors: Ameen, Taha, Yu, Sophie H.
Institution: Carnegie Mellon University
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214994840