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THE GEOMETRY OF FRACTIONAL STABLE MATCHINGS AND ITS - bschool nus

THE GEOMETRY OF FRACTIONAL STABLE MATCHINGS AND ITS - bschool nus 2025

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The document discusses the geometry of fractional stable matchings and their applications in solving stable marriage and stable roommates problems using a polyhedral approach. It introduces a new linear programming (LP) formulation for the stable roommates problem, demonstrating that a feasible solution exists if and only if there is a stable matching. The authors also present a 2-approximation algorithm for optimal solutions under specific weight functions. Additionally, they explore the structure of the stable marriage polytope, proving its integrality and discussing fairness in matchings through various objective functions. The paper contributes to understanding the feasibility of stable roommates problems and proposes valid inequalities to strengthen formulations.

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