Abstract: In barter-exchange markets, agents seek to swap their items with one another, in order to improve their own utilities. These swaps consist of cycles of agents, with each agent receiving the item of the next agent in the cycle. We focus mainly on the upcoming national kidney-exchange market, where patients with kidney disease can obtain compatible donors by swapping their own willing but incompatible donors. With over 70,000 patients already waiting for a cadaver kidney in the US, this market is seen as the only ethical way to significantly reduce the 4,000 deaths per year attributed to kidney disease.

The clearing problem involves finding a social welfare maximizing exchange when the maximum length of a cycle is fixed. Long cycles are forbidden, since, for incentive reasons, all transplants in a cycle must be performed simultaneously. Also, in barter-exchanges generally, more agents are affected if one drops out of a longer cycle. We prove that the clearing problem with this cycle-length constraint is NP-hard. Solving it exactly is one of the main challenges in establishing a national kidney exchange.

We present the first algorithm capable of clearing these markets on a nationwide scale. The key is incremental problem formulation . We adapt two paradigms for the task: constraint generation and column generation. For each, we develop techniques that dramatically improve both runtime and memory usage. We conclude that column generation scales drastically better than constraint generation. Our algorithm also supports several generalizations, as demanded by real-world kidney exchanges.

Our algorithm replaced CPLEX as the clearing algorithm of the Alliance for Paired Donation, one of the leading kidney exchanges. The match runs are conducted every two weeks and transplants based on our optimizations have already been conducted.

(Joint work with David Abraham and Avrim Blum.)

Short Bio: Tuomas Sandholm is Professor in the Computer Science Department at Carnegie Mellon University. He received the Ph.D. and M.S. degrees in computer science from the University of Massachusetts at Amherst in 1996 and 1994. He earned an M.S. (B.S. included) with distinction in Industrial Engineering and Management Science from the Helsinki University of Technology, Finland, in 1991. He has published over 250 technical papers on electronic commerce; game theory; artificial intelligence; multiagent systems; auctions and exchanges; automated negotiation and contracting; coalition formation; voting; safe exchange; normative models of bounded rationality; resource-bounded reasoning; machine learning; networks; and combinatorial optimization. He has 17 years of experience building optimization-based electronic marketplaces, and several of his systems have been commercially fielded. He is also Founder, Chairman, and Chief Scientist of CombineNet, Inc., which has fielded over 400 large-scale generalized combinatorial auctions, with over $25 billion in total spend and over $3.2 billion in generated savings. He received the National Science Foundation Career Award in 1997, the inaugural ACM Autonomous Agents Research Award in 2001, the Alfred P. Sloan Foundation Fellowship in 2003, and the IJCAI Computers and Thought Award in 2003.