Subquadratic algorithms for succinct stable matching

DOI10.1007/978-3-319-34171-2_21zbMATH Open1421.68260arXiv1510.06452OpenAlexW2923170735WikidataQ128135731 ScholiaQ128135731MaRDI QIDQ2415371

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Publication date: 21 May 2019

Published in: (Search for Journal in Brave)

Abstract: 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 $d=omega(logn)$ 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 $d$.

Full work available at URL: https://arxiv.org/abs/1510.06452

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