🤖 AI Summary
This work addresses the lack of theoretical guarantees in online matching algorithms commonly used in critical applications such as organ allocation. We propose a coarse-grained dynamic matching approach based on clustering offline nodes into capacity-constrained groups, which substantially reduces problem complexity while preserving essential structural information. For the first time, we rigorously prove that this coarse-graining strategy incurs no significant performance loss and, in fact, achieves near-optimal theoretical guarantees—thereby providing a formal foundation for clustering-based practices in organ allocation. In simulations of heart transplant allocation, our method performs nearly as well as an omniscient benchmark and significantly outperforms conventional heuristic strategies.
📝 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.