Clustering Perturbation Resilient k-Median Instances
نویسندگان
چکیده
Recently, Bilu and Linial [6] formalized an implicit assumption often made when choosing a clustering objective: that the optimum clustering to the objective should be preserved under small multiplicative perturbations to distances between points. Balcan and Liang [4] generalized this to a relaxed notion where the optimal clustering after perturbation is allowed to change slightly. In this paper, we propose an efficient algorithm for k-median instances under the generalized notion, achieving theoretical guarantees that significantly improve over previous known results. Additionally, we give a sublinear-time algorithm which can return an implicit clustering from only access to a small random sample.
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