Maximizing Expectation on Vertex-Disjoint Cycle Packing

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.