The complexity of counting stable marriages
SIAM Journal on Computing
Three fast algorithms for four problems in stable marriage
SIAM Journal on Computing
An efficient algorithm for the “optimal” stable marriage
Journal of the ACM (JACM)
Stable marriage and indifference
CO89 Selected papers of the conference on Combinatorial Optimization
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Hard variants of stable marriage
Theoretical Computer Science
The stable roommates problem with ties
Journal of Algorithms
The structure of stable marriage with indifference
Discrete Applied Mathematics
The Hospitals/Residents Problem with Ties
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Strong Stability in the Hospitals/Residents Problem
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Resource selection games with unknown number of players
AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
The stable marriage problem with master preference lists
Discrete Applied Mathematics
Guest Editorial: Special Issue on Matching Under Preferences
Algorithmica - Special Issue: Matching Under Preferences; Guest Editors: David F. Manlove, Robert W. Irving and Kazuo Iwama
When LP is the cure for your matching woes: improved bounds for stochastic matchings
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Matching with couples revisited
Proceedings of the 12th ACM conference on Electronic commerce
Proceedings of the 12th ACM conference on Electronic commerce
Elicitation and approximately stable matching with partial preferences
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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The traditional model of two-sided matching assumes that all agents fully know their own preferences. As markets grow large, however, it becomes impractical for agents to precisely assess their rankings over all agents on the other side of the market. We propose a novel model of two-sided matching in which agents are endowed with known partially ordered preferences and unknown true preferences drawn from known distributions consistent with the partial order. The true preferences are learned through interviews, revealing the pairwise rankings among all interviewed agents, performed according to a centralized interview policy, i.e., an algorithm that adaptively schedules interviews. Our goal is for the policy to guarantee both stability and optimality for a given side of the market, with respect to the underlying true preferences of the agents. As interviews are costly, we seek a policy that minimizes the number of interviews. We introduce three minimization objectives: (very weak) dominance, which minimizes the number of interviews for any underlying true preference profile; Pareto optimality, which guarantees that no other policy dominates the given policy; and optimality in expectation with respect to the preference distribution. We formulate our problem as a Markov decision process, implying an algorithm for computing an optimal-in-expectation policy in time polynomial in the number of possible preference orderings (and thus exponential in the size of the input). We then derive structural properties of dominant policies which we call optimality certificates. We show that computing a minimum optimality certificate is NP-hard, suggesting that optimal-in-expectation and/or Pareto optimal policies could be NP-hard to compute. Finally, we restrict attention to a setting in which agents on one side of the market have the same partially ordered preferences (but potentially distinct underlying true preferences), and in which agents must interview before matching. In this restricted setting, we show how to leverage the idea of minimum optimality certificates to design a computationally efficient interview-minimizing policy. This policy works without knowledge of the distributions and is dominant (and so is also Pareto optimal and optimal-in-expectation).