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arXiv · 2610.39764

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

Shuichi Miyazaki·Suguru Tamaki
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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.

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Shuichi Miyazaki, Suguru Tamaki. 2026-10-29. A Single-Exponential Time Algorithm for the Maximum-Cardinality Weakly Stable Matching Problem with Ties and Incomplete Lists. https://arxiv.org/abs/2610.39764

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