A Single-Exponential Time Algorithm for the Maximum-Cardinality Weakly Stable Matching Problem with Ties and Incomplete Lists

We study Stable Marriage with Ties and Incomplete lists (SMTI) under weak stability. For an instance with $n$ agents on each side, we give an exact algorithm that returns a maximum-cardinality weakly stable matching in $O^*(22.74^n)$ time. To the best of our knowledge, this is the first exact algorithm for this problem running in single-exponential time.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.39764
Primary Topic
Game Theory and Voting Systems
Type
preprint
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preprint

A Single-Exponential Time Algorithm for the Maximum-Cardinality Weakly Stable Matching Problem with Ties and Incomplete Lists

Shuichi Miyazaki, Suguru Tamaki
arXiv (Cornell University)
Game Theory and Voting Systems
preprint

A Single-Exponential Time Algorithm for the Maximum-Cardinality Weakly Stable Matching Problem with Ties and Incomplete Lists

Shuichi Miyazaki, Suguru Tamaki
preprint en

Abstract

We study Stable Marriage with Ties and Incomplete lists (SMTI) under weak stability. For an instance with $n$ agents on each side, we give an exact algorithm that returns a maximum-cardinality weakly stable matching in $O^*(22.74^n)$ time. To the best of our knowledge, this is the first exact algorithm for this problem running in single-exponential time.

arXiv (Cornell University)
Game Theory and Voting Systems
DOIOpen Access PDFOpenAlex
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A Single-Exponential Time Algorithm for the Maximum-Cardinality Weakly Stable Matching Problem with Ties and Incomplete Lists — Shuichi Miyazaki, Suguru Tamaki · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS