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

TL;DR

This work tackles online stochastic matching under uncertainty with a focus on organ allocation, introducing a coarsening-based framework that aggregates offline nodes into capacitated clusters and uses representative weights to obtain near-optimal guarantees. By linking to $b$-matching theory and deriving bounds that depend on cluster size $b$ and intra-cluster error $\delta(b)$, the authors provide scalable, data-driven policies that remain robust to weight estimation error $\eta$. Applying the framework to UNOS heart transplant data, they discretize donor profiles into $1000$ representative types and demonstrate a simulated competitive ratio of $0.91$, significantly outperforming baselines and the status quo while increasing transplant throughput and reducing computation. The work offers a principled bridge between data-informed heuristics and worst-case guarantees, with implications for scalability, fairness considerations, and deployment in non-stationary healthcare systems. It also discusses ethical and safety considerations, data-bias issues, and directions for future improvement in dynamic settings and bias mitigation.

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. In realistic simulations, our policy closely matches the performance of the omniscient benchmark. Our work bridges the gap between data-driven heuristics and pessimistic theoretical lower bounds, and provides rigorous justification for prior clustering-based approaches in organ allocation.

Figures (8)

• Figure 1: Left: Schematic illustration of our coarsening-based approach. Right: Competitive ratio of our algorithm compared against the post-2018 US status quo allocation for different budgets $b$ evaluated in simulation from January to June 2019.
• Figure 2: Population stability index ($\mathsf{PSI}$) of the distribution of waitlist edge weights across blood types over 2019. We report the $\mathsf{PSI}$ measured against the baseline month of January 2019 and each prior month. A $\mathsf{PSI} \le 0.1$ constitutes a stable population while a $\mathsf{PSI}\ge 0.25$ denotes major distributional shift. We take $N=10$ bins.
• Figure 3: Normalized mean absolute error of clustering algorithms across cluster sizes.
• Figure 4: Competitive ratio of our algorithm for different budgets $b$ and clustering approaches evaluated over $20$ simulations of donor arrivals from January to June 2019. The shaded region represents the standard deviation. Compared to $b=1$ and the status quo, all results are statistically significant ($p<0.05$, Wilcoxon signed-rank test).
• Figure A1: Heuristic competitive ratio of clustering algorithms across cluster sizes.

Theorems & Definitions (13)

• Theorem 1: Brubach16:New
• Theorem 3
• Theorem 5
• Theorem 7
• Remark 8
• Theorem 8: Brubach16:New
• proof
• Theorem 8
• proof
• Theorem 9