Half-cycle: A new formulation for modelling kidney exchange problems

We introduce the half-cycle formulation (HCF), a new integer programming (IP) model for kidney exchange problem, which has life-saving applications. In HCF, cycle (i.e., set of swaps) is represented by two compatible halves. After giving several algorithmic enhancements we show through extensive computational experiments with an IP solver that our outperforms existing formulations when size limit to 4, 5, or 6, depending on density compatibility graph.