Work

The strongly stable roommates problem and linear programming

Year: 2026

Type: article

Abstract: The stable roommates problem is a non-bipartite version of the stable matching problem in a bipartite graph. In this paper, we consider the stable roommates problem with ties. In particular, we focus on strong stability, which is one of the main stability concepts in the stable roommates problem with ties. We propose a new polynomial-time algorithm for the problem of checking the existence of a strongly stable matching in the stable roommates problem with ties. More concretely, we extend the linear programming approach of Abeledo and Blum to the stable roommates problem with strict preferences to our problem.

Source: Discrete Optimization

DOI: 10.1016/j.disopt.2026.100969

Author: Naoyuki Kamiyama

Institution: Kyoto University

Language: English

Topic: Game Theory and Voting Systems

Subfield: Economics and Econometrics

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $2,760

Funders: Japan Science and Technology Agency, Exploratory Research for Advanced Technology