Maximizing Expectation on Vertex-Disjoint Cycle Packing

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.

[1]  Frank Harary,et al.  Graphical enumeration , 1973 .

[2]  Miguel Constantino,et al.  New insights on integer-programming models for the kidney exchange problem , 2013, Eur. J. Oper. Res..

[3]  Yan Zhou,et al.  Graph-Based Optimization Algorithm and Software on Kidney Exchanges , 2012, IEEE Transactions on Biomedical Engineering.

[4]  M. Utku Ünver,et al.  Dynamic Kidney Exchange , 2007 .

[5]  John D. Kalbfleisch,et al.  Optimization and Simulation of an Evolving Kidney Paired Donation (KPD) Program , 2011 .

[6]  M. Utku Ünver,et al.  Increasing the Opportunity of Live Kidney Donation by Matching for Two- and Three-Way Exchanges , 2006, Transplantation.

[7]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[8]  Avrim Blum,et al.  Clearing algorithms for barter exchange markets: enabling nationwide kidney exchanges , 2007, EC '07.

[9]  J. Edmonds.  Paths, Trees, and Flowers , 1965, Canadian Journal of Mathematics.

[10]  Frank Harary,et al.  A Survey of Graphical Enumeration Problems††Work supported in part by grants from the Air Force Office of Scientific Research and the National Science Foundation. , 1973 .

[11]  Harold W. Kuhn,et al.  The Hungarian method for the assignment problem , 1955, 50 Years of Integer Programming.

[12]  Tayfun Sönmez,et al.  Market Design for Kidney Exchange , 2011 .

[13]  Ariel D. Procaccia,et al.  Optimizing kidney exchange with transplant chains: theory and reality , 2012, AAMAS.