Biro, P., Manlove, D.F. and Rizzi, R. (2009) Maximum weight cycle packing in directed graphs, with application to kidney exchange programs. Discrete Mathematics, Algorithms and Applications, 1(4), pp. 499-517. (doi: 10.1142/S1793830909000373)
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Abstract
Centralized matching programs have been established in several countries to organize kidney exchanges between incompatible patient-donor pairs. At the heart of these programs are algorithms to solve kidney exchange problems, which can be modelled as cycle packing problems in a directed graph, involving cycles of length 2, 3, or even longer. Usually, the goal is to maximize the number of transplants, but sometimes the total benefit is maximized by considering the differences between suitable kidneys. These problems correspond to computing cycle packings of maximum size or maximum weight in directed graphs. Here we prove the APX-completeness of the problem of finding a maximum size exchange involving only 2-cycles and 3-cycles. We also present an approximation algorithm and an exact algorithm for the problem of finding a maximum weight exchange involving cycles of bounded length. The exact algorithm has been used to provide optimal solutions to real kidney exchange problems arising from the National Matching Scheme for Paired Donation run by NHS Blood and Transplant, and we describe practical experience based on this collaboration.
Item Type: | Articles |
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Additional Information: | Electronic version of an article published as Discrete Mathematics, Algorithms and Applications 1(4):499-517, 2009. DOI: 10.1142/S1793830909000373 © World Scientific Publishing Company [http://www.worldscinet.com/dmaa/dmaa.shtml] |
Keywords: | Directed graph, triangle packing, APX-completeness, approximation algorithm, exact algorithm, kidney paired donation |
Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Manlove, Professor David and Biro, Dr Peter |
Authors: | Biro, P., Manlove, D.F., and Rizzi, R. |
Subjects: | Q Science > QA Mathematics > QA75 Electronic computers. Computer science |
College/School: | College of Science and Engineering > School of Computing Science |
Journal Name: | Discrete Mathematics, Algorithms and Applications |
Publisher: | World Scientific Publishing |
ISSN: | 1793-8309 |
ISSN (Online): | 1793-8317 |
Copyright Holders: | Copyright © 2009 World Scientific Publishing |
First Published: | First published in Discrete Mathematics, Algorithms and Applications 1(4):499-517 |
Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher. |
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