Optimizing for Fairness in Generalized Kidney Exchange: Theory and Computations
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| Format: | Preprint |
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2026
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| _version_ | 1866913146539606016 |
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| author | Chang, Claire Khare, Arin Shmoys, David |
| author_facet | Chang, Claire Khare, Arin Shmoys, David |
| contents | The seminal work of Roth, Sönmez, & Ünver shows that the Edmonds-Gallai structure theorem for non-bipartite matching can be leveraged to yield a randomized algorithm to match patient-donor pairs in kidney exchange with extraordinarily strong properties. This breakthrough led to randomized polynomial-time algorithms to find a maximum-cardinality matching maximizing individual fairness objectives--measured by the probability that nodes are matched--such as Nash social welfare. But the exchanges allowed in practice go beyond cardinality matching, generalizing to weighted variants and allowing structures such as paths and 3-cycles. We show that strongly polynomial algorithms guaranteeing the same fairness properties can be obtained in weighted settings for matching and 2-paths. While even maximum cardinality coverage with cycles and paths of length at least three is NP-hard, we provide a general result showing that any optimization subroutine (for whichever structure is allowed) can be bootstrapped using a polynomial number of calls to yield a mechanism that has analogous fairness properties to those obtained for matching. We complement these theoretical results with computational results, both on well-studied synthetic data-sets and on samples drawn from real data, that demonstrate the striking advantages of adding fairness considerations to more general kidney-exchange mechanisms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_20070 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimizing for Fairness in Generalized Kidney Exchange: Theory and Computations Chang, Claire Khare, Arin Shmoys, David Data Structures and Algorithms Optimization and Control The seminal work of Roth, Sönmez, & Ünver shows that the Edmonds-Gallai structure theorem for non-bipartite matching can be leveraged to yield a randomized algorithm to match patient-donor pairs in kidney exchange with extraordinarily strong properties. This breakthrough led to randomized polynomial-time algorithms to find a maximum-cardinality matching maximizing individual fairness objectives--measured by the probability that nodes are matched--such as Nash social welfare. But the exchanges allowed in practice go beyond cardinality matching, generalizing to weighted variants and allowing structures such as paths and 3-cycles. We show that strongly polynomial algorithms guaranteeing the same fairness properties can be obtained in weighted settings for matching and 2-paths. While even maximum cardinality coverage with cycles and paths of length at least three is NP-hard, we provide a general result showing that any optimization subroutine (for whichever structure is allowed) can be bootstrapped using a polynomial number of calls to yield a mechanism that has analogous fairness properties to those obtained for matching. We complement these theoretical results with computational results, both on well-studied synthetic data-sets and on samples drawn from real data, that demonstrate the striking advantages of adding fairness considerations to more general kidney-exchange mechanisms. |
| title | Optimizing for Fairness in Generalized Kidney Exchange: Theory and Computations |
| topic | Data Structures and Algorithms Optimization and Control |
| url | https://arxiv.org/abs/2605.20070 |