An efficient algorithm to enumerate sets with fallbacks in a kidney paired donation program

Abstract

Kidney paired donation is a partial solution to overcoming biological incompatibility preventing kidney transplants. A kidney paired donation (KPD) program consists of altruistic or non-directed donors (NDDs) and pairs, each of which comprises a candidate in need of a kidney transplant and her/his willing but incompatible donor. Potential transplants from NDDs or donors in pairs to compatible candidates in other pairs are determined by computer assessment, though various situations involving either the donor, candidate, or proposed transplant may lead to a potential transplant failing to proceed. A KPD program can be viewed as a directed graph with NDDs and pairs as vertices and potential transplants as edges, where failure probabilities are associated with each vertex and edge. Transplants are carried out in the form of directed cycles among pairs and directed paths initiated by NDDs, which we refer to respectively as cycles and chains. Previous research shows that selecting disjoint subgraphs with a view to creating fallback options when failures occur generates more realized transplants than optimal selection of disjoint chains and cycles. In this paper, we define such subgraphs, which are called locally relevant (LR) subgraphs, and present an efficient algorithm to enumerate all LR subgraphs. Its computational efficiency is significantly better than the previous, more restrictive, algorithms.

Kidney Exchange with Inhomogeneous Edge Existence Uncertainty

“…Several other optimization-based approaches have been proposed, using recourse [Anderson et al, 2015], forms of "fallback" options [Bartier et al, 2019, Manlove and O'Malley, 2015, Wang et al, 2019, and pre-match edge queries [Blum et al, 2013, McElfresh et al, 2020. These methods involve additional decision stages, and are not directly comparable in our setting.…”

KPDGUI: An interactive application for optimization and management of a virtual kidney paired donation program

“…The size of the sets of interest in previous studies are limited, with no explicit consideration for NDDs. The sets of interest here are formally defined and more thoroughly examined in Wang et al [26], where methods of enumeration are also developed. Again, after accounting for donor, candidate, and match viability within each LRS, one proceeds with the best remaining set of sub-cycles and sub-chains within each subgraph..…”

“…Previous research suggests including, along with the utilities, probabilities that selected exchanges might eventually be found to be non-viable, whereby the KPD solution consists of exchanges that maximize the expected utility [17,18,[21][22][23]. Optimization can be further extended beyond selection of simple cycles or chains to encompass fallback options in case of non-viability [24][25][26]. We have previously investigated the incorporation of these considerations into KPD optimization through simulation, where formidable gains in realized utility were observed [27,28].…”