Clustering with faulty centers

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2023-08-21 DOI:10.1016/j.comgeo.2023.102052

Emily Fox , Hongyao Huang , Benjamin Raichel

引用次数: 0

Abstract

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 $(1 + ε)$ -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.

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具有故障中心的聚类

在本文中，我们引入并正式研究了具有故障中心的k-聚类问题。具体来说，我们研究了k-中心、k-中值和k-均值聚类的错误版本，其中中心有一定的不存在概率，而之前的工作中客户端有一定的可能性不存在。对于这三个问题，我们提供了固定参数的可处理算法，在参数k、d和ε中，（1+ε）-近似于d维欧氏空间中点的最小期望成本解。对于故障k中心，我们还提供了一般度量的5近似值。值得注意的是，我们所有的算法对n只有线性依赖关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Geometry-Theory and Applications 数学-数学

CiteScore

1.60

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in all areas of the subject, as well as disseminating information on the applications, techniques, and use of computational geometry. Computational Geometry publishes articles on the design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects. Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems. Computational Geometry features a special section containing open problems and concise reports on implementations of computational geometry tools.