At most 3.55nstable matchings

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Abstract

We improve the upper bound for the maximum possible number of stable matchings among n jobs and n applicants from 131072n+ O(1) to 3.55n+ O(1). To establish this bound, we state a novel formulation of a certain entropy bound that is easy to apply and may be of independent interest in counting other combinatorial objects.

Original languageEnglish
Title of host publicationProceedings - 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science, FOCS 2021
PublisherIEEE Computer Society
Pages217-227
Number of pages11
ISBN (Electronic)9781665420556
DOIs
StatePublished - 2022
Event62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021 - Virtual, Online, United States
Duration: Feb 7 2022Feb 10 2022

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2022-February
ISSN (Print)0272-5428

Conference

Conference62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021
Country/TerritoryUnited States
CityVirtual, Online
Period02/7/2202/10/22

Funding

We would like to thank Padmini Mukkamala for pointing out Claim 15, Viktor Harangi and Gábor Kun for discussions about other proofs of Lemma 4, Ágnes Cseh for calling our attention to relevant literature about stable matchings, and Balázs Patkós for comments on the first version of this paper. This work has started while the first author visited the second at Eötvös Loránd University, supported by grant number LP2017-19/2017 of the Lendület program of the Hungarian Academy of Sciences (MTA).

Funders
Mount Allison University

    Keywords

    • entropy
    • stable matchings

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