Reproduce “Small Representations of Big Kidney Exchange Graphs” on OpenResearch
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About this paper
John P. Dickerson, Aleksandr M. Kazachkov, Ariel D. Procaccia, Tuomas Sandholm
The paper introduces an attribute-based model for kidney exchange compatibility graphs, demonstrating that central NP-hard matching problems become polynomially solvable when graphs can be represented with a constant number of attributes. Empirical analysis on real UNOS data shows these graphs can be represented with a small number of attributes, and slightly relaxing compatibility criteria significantly increases transplant efficiency, with matching rates approaching 100% at a threshold of 5.
Key insights
- NP-hard kidney exchange matching problems can be solved in polynomial time if compatibility graphs can be represented using a constant number of patient and donor attributes.
- The problem of finding an optimal $(k,t)$-representation for a general graph, especially with ignored edges, is NP-complete, indicating computational challenges in deriving attribute sets directly.
- Allowing even a small, thresholded number of attribute conflicts (negative interactions) between donor and patient can lead to substantial gains in matching efficiency.
Summary by alphaXiv.
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