The strongly stable roommates problem and linear programming
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.
Fields of Study & Subjects
Game Theory and Voting Systems
Optimization and Search Problems
Optimization and Variational Analysis
Publication details
- Journal / source
- Discrete Optimization
- Publisher
- Elsevier BV
- Volume
- 62
- Pages
- 100969–100969
- Publication date
- 13 September 2026
- Language
- EN