The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Stable marriage and indifference
CO89 Selected papers of the conference on Combinatorial Optimization
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Hard variants of stable marriage
Theoretical Computer Science
Stable Marriage with Incomplete Lists and Ties
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Strong Stability in the Hospitals/Residents Problem
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Strongly stable matchings in time O(nm) and extension to the hospitals-residents problem
ACM Transactions on Algorithms (TALG)
Competitive equilibria in matching markets with budgets
ACM SIGecom Exchanges
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An instance of the stable assignment problem consists of a bipartite graph with arbitrary node and edge capacities, and arbitrary preference lists (allowing both ties and incomplete lists) over the set of neighbors. An assignment is strongly stable if there is no blocking pair where one member of the pair strictly prefers the other member to some partner in the current assignment, and the other weakly prefers the first to some partner in its current assignment. We give a strongly polynomial time algorithm to determine the existence of a strongly stable assignment, and compute one if it exists. The central component of our algorithm is a generalization of the notion of the critical set in bipartite matchings to the critical subgraph in bipartite assignment; this generalization may be of independent interest.