For Stable Hypergraph Matching, College Admission with Common Quotas, and Stable Multicommodity Flow, a stable matching always exists after perturbing capacities by at most ℓ-1, 2ℓ-1, or k-1, respectively.
Journal of Algorithms 12, 1 (1991), 154–178
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Near-Feasible Solutions to Complex Stable Matching Problems
For Stable Hypergraph Matching, College Admission with Common Quotas, and Stable Multicommodity Flow, a stable matching always exists after perturbing capacities by at most ℓ-1, 2ℓ-1, or k-1, respectively.