Near-Optimal Dynamic Matching via Coarsening with Application to Heart Transplantation

TL;DR

This paper introduces a coarsening-based online matching algorithm that achieves near-optimal performance, demonstrated through application to heart transplant allocation with real data simulations.

Contribution

It presents a novel coarsening approach for online matching that provides strong theoretical guarantees and practical policies for organ allocation.

Findings

Achieves a competitive ratio of 0.91 in simulations, outperforming the US policy's 0.51.

Provides near-optimal theoretical guarantees through node aggregation.

Bridges the gap between data-driven heuristics and theoretical bounds.

Abstract

Online matching has been a mainstay in domains such as Internet advertising and organ allocation, but practical algorithms often lack strong theoretical guarantees. We take an important step toward addressing this by developing new online matching algorithms based on a coarsening approach. Although coarsening typically implies a loss of granularity, we show that, to the contrary, aggregating offline nodes into capacitated clusters can yield near-optimal theoretical guarantees. We apply our methodology to heart transplant allocation to develop theoretically grounded policies based on structural properties of historical data. Furthermore, in simulations based on real data, our policy closely matches the performance of the omniscient benchmark, achieving competitive ratio 0.91, drastically higher than the US status quo policy's 0.51. Our work bridges the gap between data-driven heuristics and pessimistic theoretical lower bounds.