The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
The iSLIP scheduling algorithm for input-queued switches
IEEE/ACM Transactions on Networking (TON)
A sublinear parallel algorithm for stable matching
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Matching Output Queueing with a Combined Input Output Queued Switch
Matching Output Queueing with a Combined Input Output Queued Switch
Collaboration of untrusting peers with changing interests
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
Collaborate with strangers to find own preferences
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Online collaborative filtering with nearly optimal dynamic regret
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
The stable marriage problem with master preference lists
Discrete Applied Mathematics
Competitive collaborative learning
Journal of Computer and System Sciences
A Note on Distributed Stable Matching
ICDCS '09 Proceedings of the 2009 29th IEEE International Conference on Distributed Computing Systems
Distributed stable matching problems with ties and incomplete lists
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
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The Stable Matching problem was introduced by Gale and Shapley in 1962. The input for the stable matching problem is a complete bipartite Kn,n graph together with a ranking for each node. Its output is a matching that does not contain a blocking pair, where a blocking pair is a pair of elements that are not matched together but rank each other higher than they rank their current mates. In this work we study the Distributed Weighted Stable Matching problem. The input to the Weighted Stable Matching problem is a complete bipartite Kn,n graph and a weight function W. The ranking of each node is determined by W, i.e. node v prefers node u1 over node u2 if W((v,u1))W((v, u2)). Using this ranking we can solve the original Stable Matching problem. We consider two different communication models: the billboard model and the full distributed model. In the billboard model, we assume that there is a public billboard and each participant can write one message on it in each time step. In the distributed model, we assume that each node can send O(logn) bits on each edge of the Kn,n. In the billboard model we prove a somewhat surprising tight bound: any algorithm that solves the Stable Matching problem requires at least n−1 rounds. We provide an algorithm that meets this bound. In the distributed communication model we provide an algorithm named intermediation agencies algorithm, in short (IAA), that solves the Distributed Weighted Stable Marriage problem in $O(\sqrt{n})$ rounds. This is the first sub-linear distributed algorithm that solves some subcase of the general Stable Marriage problem.