Fast Core Identification

A new paper by Irene Aldridge presents a significant advance in matching market algorithms. The work proves that the Core Identification Problem (CIP) — determining which agents receive a core allocation under the Top Trading Cycles (TTC) mechanism — can be solved in O(Ln) time, where L is the maximum number of preferences reported per agent. For sparse preference profiles like NYC school choice (where L = 12), this yields an O(n) algorithm, strictly improving on the O(n log n) complexity of full TTC allocation. The method uses a randomized SVD to compute the leading eigenvector of a preference-derived Markov transition matrix, achieving asymptotic optimality by matching the information-theoretic lower bound of Ω(n).

Crucially, the algorithm inherits all desirable properties of TTC: Pareto efficiency, individual rationality, and strategy-proofness. It also shows robustness to preference noise for sufficiently large n. This means that for large-scale matching markets (e.g., school choice, kidney exchange, or housing allocation), identifying who gets a core allocation can now be done in linear time, making it practical for real-time or near-real-time applications. The paper is 23 pages and is available on arXiv under cs.GT and econ.TH categories, with ACM class H.4.