Fair Pairwise Exchange among Groups

Abstract

We study the pairwise organ exchange problem among groups motivated by real-world applications and consider two types of group formulations. Each group represents either a certain type of patient-donor pairs who are compatible with the same set of organs, or a set of patient-donor pairs who reside in the same region. We address a natural research question, which asks how to match a maximum number of pairwise compatible patient-donor pairs in a fair and individually rational way. We first propose a natural fairness concept that is applicable to both types of group formulations and design a polynomial-time algorithm that checks whether a matching exists that satisfies optimality, individual rationality, and fairness. We also present several running time upper bounds for computing such matchings for different graph structures.

Partitioned Matching Games for International Kidney Exchange

“…However, Abraham, Blum and Sandholm [1] proved that already for ℓ = 3 it becomes NP-hard to find an optimal solution for a round. We therefore set ℓ = 2 1 , just like some related papers [14,15,35], which we discuss later.…”

“…They gave a polynomial-time algorithm for computing a Nash-equilibrium that maximizes the total number of transplants, improving the previously known result of [15] for two countries. Sun et al [35] also considered 2-way exchanges only. They defined so-called selection ratios using various lower and upper target numbers of kidney transplants for each country.…”

“…In contrast to [14,15,35], we model an IKEP as follows. Consider a directed compatibility graph G = (V, A) with a positive arc weighting w.…”

Computing Balanced Solutions for Large International Kidney Exchange Schemes

“…Sun et al [37] also considered 2-way exchanges only. They defined so-called selection ratios using various lower and upper target numbers of kidney transplants for each country.…”

“…In Section 2 we explain the credit system of [12,15,31] and our settings. We only allow 2-way exchanges (just as [19,20,37], but unlike [12,31]) and do not consider weights (just as [12,31]). In Section 3, we generalize the above polynomial-time result of [15] by giving a polynomial-time algorithm for computing a maximum matching that lexicographically minimizes the country deviations from a given target allocation.…”