Subquadratic Algorithms for Succinct Stable Matching

We consider the stable matching problem when the preference lists are not given explicitly but are represented in a succinct way and ask whether the problem becomes computationally easier and investigate other implications. We give subquadratic algorithms for finding a stable matching in special cases of natural succinct representations of the problem, the d -attribute, d -list, geometric, and single-peaked models. We also present algorithms for verifying a stable matching in the same models. We further show that for d = ω ( log n ) both finding and verifying a stable matching in the d -attribute and d -dimensional geometric models requires quadratic time assuming the Strong Exponential Time Hypothesis. This suggests that these succinct models are not significantly simpler computationally than the general case for sufficiently large d .