Kidney exchange and endless paths: On the optimal use of an altruistic donor

TL;DR

This paper develops efficient algorithms for kidney exchange with altruistic donors, achieving optimal expected waiting times and extending results to multiple donors, thereby improving the theoretical understanding and practical performance of such systems.

Contribution

It introduces linear-time algorithms with optimal expected waiting times, simplifies previous analyses, and extends results to multiple altruistic donors in kidney exchange models.

Findings

Algorithms achieve O(1/p) expected waiting time

Guarantees hold with high probability for all patients

Results extend to multiple altruistic donors

Abstract

We consider a well-studied online random graph model for kidney exchange, where nodes representing patient-donor pairs arrive over time, and the probability of a directed edge is p. We assume existence of a single altruistic donor, who serves as a start node in this graph for a directed path of donations. The algorithmic problem is to select which donations to perform, and when, to minimize the amount of time that patients must wait before receiving a kidney. We advance our understanding of this setting by (1) providing efficient (in fact, linear-time) algorithms with optimal O(1/p) expected waiting time, (2) showing that some of these algorithms in fact provide guarantees to all patients of O(1/p) waiting time {\em with high probability}, (3) simplifying previous analysis of this problem, and (4) extending results to the case of multiple altruistic donors.