A constant-factor approximation algorithm for the k-median problem (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximation algorithms
Clustering with Qualitative Information
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Machine Learning
A survey on clustering algorithms for wireless sensor networks
Computer Communications
On Strong Equilibria in the Max Cut Game
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Computing stable outcomes in hedonic games
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
An O(pn2) algorithm for the p -median and related problems on tree graphs
Operations Research Letters
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Clustering, the partitioning of objects with respect to a similarity measure, has been extensively studied as a global optimization problem. We investigate clustering from a game theoretic approach, and consider the class of hedonic clustering games. Here, a self organized clustering is obtained via decisions made by independent players, corresponding to the elements clustered. Being a hedonic setting, the utility of each player is determined by the identity of the other members of her cluster. This class of games seems to be quite robust, as it fits with rather different, yet commonly used, clustering criteria. Specifically, we investigate hedonic clustering games in two different models: fixed clustering, which subdivides into k-median and k-center, and correlation clustering. We provide a thorough and non-trivial analysis of these games, characterizing Nash equilibria, and proving upper and lower bounds on the price of anarchy and price of stability. For fixed clustering we focus on the existence of a Nash equilibrium, as it is a rather non-trivial issue in this setting. We study it both for general metrics and special cases, such as line and tree metrics. In the correlation clustering model, we study both minimization and maximization variants, and provide almost tight bounds on both price of anarchy and price of stability.