Abstract
This paper proposes a method for computing the expectation for the length of a maximum set of vertex-disjoint cycles in a digraph where vertices and/or arcs are subject to failure with a known probability. This method has an immediate practical application: it can be used for the solution of a kidney exchange program in the common situation where the underlying graph is unreliable. Results for realistic benchmark instances are reported and analyzed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Li, Y., Kalbfleisch, J., Song, P.X., Zhou, Y., Leichtman, A., Rees, M.: Optimization and simulation of an evolving kidney paired donation (KPD) program. Working Paper Series 90, Department of Biostatistics, University of Michigan (May 2011), http://www.bepress.com/umichbiostat/paper90
Constantino, M., Klimentova, X., Viana, A., Rais, A.: New insights on integer-programming models for the kidney exchange problem. European Journal of Operational Research 231(1), 57–68 (2013)
Chen, Y., Li, Y., Kalbfleisch, J.D., Zhou, Y., Leichtman, A., Song, P.X.K.: Graph-based optimization algorithm and software on kidney exchanges. IEEE Trans. Biomed. Engineering 59(7), 1985–1991 (2012)
Ünver, M.U.: Dynamic kidney exchange. Review of Economic Studies 77(1), 372–414 (2010)
Sönmez, T., Ünver, M.U.: Market Design for Kidney Exchange. In: Oxford Handbook of Market Design. Oxford University Press (2013)
Dickerson, J.P., Procaccia, A.D., Sandholm, T.: Optimizing kidney exchange with transplant chains: theory and reality. In: van der Hoek, W., Padgham, L., Conitzer, V., Winikoff, M. (eds.) AAMAS, pp. 711–718. IFAAMAS (2012)
Abraham, D.J., Blum, A., Sandholm, T.: Clearing algorithms for barter exchange markets: enabling nationwide kidney exchanges. In: MacKie-Mason, J.K., Parkes, D.C., Resnick, P. (eds.) ACM Conference on Electronic Commerce, pp. 295–304. ACM (2007)
Edmonds, J.: Paths, trees, and flowers. Canadian Journal of Mathematics. Journal Canadien de Mathématiques 17, 449–467 (1965)
Kuhn, H.W.: The Hungarian Method for the assignment problem. Naval Research Logistics Quarterly 2, 83–97 (1955)
Harary, F., Palmer, E.M.: Graphical Enumeration. Academic Press, New York (1973)
Saidman, S.L., Roth, A.E., Sönmez, T., Ünver, M.U., Delmonico, F.L.: Increasing the opportunity of live kidney donation by matching for two- and three-way exchanges. Transplantation 81, 773–782 (2006)
Gurobi Optimization, Inc.: Gurobi Optimizer Reference Manual, Version 5.0 (2012), http://www.gurobi.com
Wolfram Research, Inc.: Mathematica. Version 8.0 edn. Wolfram Research, Inc., Champaign, Illinois (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Pedroso, J.P. (2014). Maximizing Expectation on Vertex-Disjoint Cycle Packing. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2014. ICCSA 2014. Lecture Notes in Computer Science, vol 8580. Springer, Cham. https://doi.org/10.1007/978-3-319-09129-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-09129-7_3
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09128-0
Online ISBN: 978-3-319-09129-7
eBook Packages: Computer ScienceComputer Science (R0)