Clustering with or without the Approximation

We study algorithms for clustering data that were recently proposed by Balcan, Blum and Gupta in SODA’09 [4] and that have already given rise to two follow-up papers. The input for the clustering problem consists of points in a metric space and a number k, specifying the desired number of clusters. The algorithms find a clustering that is provably close to a target clustering, provided that the instance has the “(1 + α, ε)-property”, which means that the instance is such that all solutions to the k-median problem for which the objective value is at most (1 + α) times the optimal objective value correspond to clusterings that misclassify at most an ε fraction of the points with respect to the target clustering. We investigate the theoretical and practical implications of their results. Our main contributions are as follows. First, we show that instances that have the (1+α, ε)-property and for which, additionally, the clusters in the target clustering are large, are easier t...

• Type: Conference
• Year: 2010
• Where: COCOON
• Authors: Frans Schalekamp, Michael Yu, Anke van Zuylen
• Keywords: Algorithm, COCOON 2010, Combinatorics, Data Set, Target Clustering