In this paper we introduce and formally study the problem of k-clustering with faulty centers. Specifically, we study the faulty versions of k-center, k-median, and k-means clustering, where centers have some probability of not existing, as opposed to prior work where clients had some probability of not existing. For all three problems we provide fixed parameter tractable algorithms, in the parameters k, d, and ε, that $(1+\epsilon )$-approximate the minimum expected cost solutions for points in d dimensional Euclidean space. For Faulty k-center we additionally provide a 5-approximation for general metrics. Significantly, all of our algorithms have only a linear dependence on n.

在本文中，我们介绍并正式研究了具有错误中心的k聚类问题。具体来说，我们研究了k中心、k中位数和k均值聚类的错误版本，其中中心有一定概率不存在，这与之前的工作（客户端有一定概率不存在）相反。对于所有三个问题，我们提供固定参数的易处理算法，在参数k、d和ε中，$（1+\epsilon ）$- d维欧几里德空间中点的近似最小预期成本解决方案。对于有缺陷的k中心，我们还为一般指标提供了 5 近似值。值得注意的是，我们所有的算法仅对n具有线性依赖性。