Maximum weight cycle packing in directed graphs, with application to kidney exchange programs

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
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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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
320021Algorithmics of Stable Matching Problems with IndifferenceDavid ManloveEngineering & Physical Sciences Research Council (EPSRC)GR/R84597/01Computing Science
436361MATCH-UP - matching under preferences - algorithms and complexityRobert IrvingEngineering & Physical Sciences Research Council (EPSRC)EP/E011993/1COM - COMPUTING SCIENCE