If a donor is not a good match for a kidney transplant recipient, the donor/recipient pair can be combined with other pairs to find a sequence of pairings that is more effective. The group of donor/recipient pairs, with information on the potential effectiveness of each match, forms a weighted bipartite graph. The Hungarian Algorithm allows us to find an optimal matching for such a graph, but the optimal outcome for the group might not be the most equitable for the individual patients involved. We examine several modifications to the Hungarian method which consider a balance between the optimal score for the group and the most uniformly equitable score for the individuals.
Patti Frazer Lock, Cummings Professor of Mathematics, Department of Mathematics, Computer Science, and Statistics, St. Lawrence University
Montgomery, Robert John
"Kidney Paired Donation: Optimal and Equitable Matchings in Bipartite Graphs,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 17
, Article 11.
Available at: http://scholar.rose-hulman.edu/rhumj/vol17/iss1/11