文章基本信息
- 标题：Preclustering Algorithms for Imprecise Points
- 本地全文：下载
- 作者：Mohammad Ali Abam ; Mark de Berg ; Sina Farahzad 等
- 期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
- 电子版ISSN：1868-8969
- 出版年度：2020
- 卷号：162
- 页码：3:1-3:12
- DOI：10.4230/LIPIcs.SWAT.2020.3
- 出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
- 摘要：We study the problem of preclustering a set B of imprecise points in â"^d: we wish to cluster the regions specifying the potential locations of the points such that, no matter where the points are located within their regions, the resulting clustering approximates the optimal clustering for those locations. We consider k-center, k-median, and k-means clustering, and obtain the following results. Let B:={bâ,,â¦,b_n} be a collection of disjoint balls in â"^d, where each ball b_i specifies the possible locations of an input point p_i. A partition ð'Z of B into subsets is called an (f(k),α)-preclustering (with respect to the specific k-clustering variant under consideration) if (i) ð'Z consists of f(k) preclusters, and (ii) for any realization P of the points p_i inside their respective balls, the cost of the clustering on P induced by ð'Z is at most α times the cost of an optimal k-clustering on P. We call f(k) the size of the preclustering and we call α its approximation ratio. We prove that, even in â"^1, one may need at least 3k-3 preclusters to obtain a bounded approximation ratio - this holds for the k-center, the k-median, and the k-means problem - and we present a (3k,1) preclustering for the k-center problem in â"^1. We also present various preclusterings for balls in â"^d with d⩾2, including a (3k,α)-preclustering with αâ^13.9 for the k-center and the k-median problem, and αâ^254.7 for the k-means problem.
- 关键词：Geometric clustering; k-center; k-means; k-median; imprecise points; approximation algorithms
