The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
On-line algorithms for weighted bipartite matching and stable marriages
Theoretical Computer Science
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
Approximability results for stable marriage problems with ties
Theoretical Computer Science
A theory of competitive analysis for distributed algorithms
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Social Networks and Stable Matchings in the Job Market
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
The stable roommates problem with globally-ranked pairs
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Almost Stable Matchings by Truncating the Gale–Shapley Algorithm
Algorithmica - Special Issue: Matching Under Preferences; Guest Editors: David F. Manlove, Robert W. Irving and Kazuo Iwama
Local matching dynamics in social networks
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
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We study the dynamics of a social network. Each node has to decide locally which other node it wants to befriend, i.e., to which other node it wants to create a connection in order to maximize its welfare, which is defined as the sum of the weights of incident edges. This allows us to model the cooperation between nodes where every node tries to do as well as possible. With the limitation that each node can only have a constant number of friends, we show that every local algorithm is arbitrarily worse than a globally optimal solution. Furthermore, we show that there cannot be a best local algorithm, i.e., for every local algorithm exists a social network in which the algorithm performs arbitrarily worse than some other local algorithm. However, one can combine a number of local algorithms in order to be competitive with the best of them. We also investigate a slightly different valuation variant. Nodes include another node's friends for their valuation. There are scenarios in which this does not converge to a stable state, i.e., the nodes switch friends indefinitely.