Finalizing tentative matches from truncated preference lists
Hisao Tamaki

TL;DR
This paper investigates the problem of determining whether tentative matches in truncated preference lists are finalizable, revealing computational complexity results and providing algorithms for specific cases in stable matching scenarios.
Contribution
It introduces the FTM problem, proves its coNP-completeness, and offers polynomial-time algorithms for resident-minimal instances with certain constraints.
Findings
FTM is coNP-complete even with hospitals of quota 1.
Polynomial-time algorithm for FTM in resident-minimal instances with hospital quota 1.
FTM remains coNP-complete for resident-minimal instances when hospital quota ≥ 2.
Abstract
Consider the standard hospitals/residents problem, or the two-sided many-to-one stable matching problem, and assume that the true preference lists of both sides are complete and strict. The lists actually submitted, however, are truncated. Let I be such a truncated instance. When we apply the resident-proposing deferred acceptance algorithm of Gale and Shapley to I, the algorithm produces a set of tentative matches (resident-hospital pairs). We say that a tentative match in this set is finalizable in I if it is in the resident-optimal stable matching for every completion of I (a complete instance of which I is a truncation). We study the problem we call FTM (Finalizability of Tentative Matches) of deciding if a given tentative match is finalizable in a given truncated instance. We first show that FTM is coNP-complete, even in the stable marriage case where the quota of each hospital is…
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Taxonomy
TopicsGame Theory and Voting Systems · Data Management and Algorithms · Bayesian Modeling and Causal Inference
