The Need for (long) Chains in Kidney Exchange

That's the title of a new paper that explores (using random graph theory) the dramatic success of long non-simultaneous chains in kidney exchange (aka kidney paired donation), since the first one was organized by Michael Rees through the Alliance for Paired Donation. They are a big part of the success of Garet Hil's National Kidney Registry as well.

Here's the paper: The Need for (long) Chains in Kidney Exchange
by Itai Ashlagi David Gamarnik Michael A. Rees Alvin E. Roth

Abstract
It has been previously shown that for sufficiently large pools of patient-donor pairs, (almost) efficient kidney exchange can be achieved by using at most 3-way cycles, i.e. by using cycles among no more than 3 patient-donor pairs. However, as kidney exchange has grown in practice, cycles among n > 3 pairs have proved useful, and long chains initiated by non-directed, altruistic donors have proven to be very effective. 


We explore why this is the case, both empirically and theoretically. We provide an analytical model of exchange when there are many highly sensitized patients, and show that large cycles of exchange or long chains can significantly increase efficiency when the opportunities for exchange are sparse. As very large cycles of exchange cannot be used in practice, long non-simultaneous chains initiated by non-directed donors significantly increase efficiency in patient pools of the size and composition that presently exist. Most importantly, long chains benefit highly sensitized patients without harming low-sensitized patients.