A PTAS for One Cardinality-Weighted 2-Clustering Problem

  • Anna PanasenkoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11548)


We consider one strongly NP-hard problem of clustering a finite set of points in Euclidean space. In this problem, we need to partition a finite set of points into two clusters minimizing the sum over both clusters of the weighted intracluster sums. Each of these sums is the sum of squared distances between the elements of the cluster and their center. The center of the one cluster is unknown and determined as the centroid, while the center of the other one is fixed at the origin. The weight factors for both intracluster sums are the given sizes of the clusters. In this paper, we present an approximation algorithm for the problem and prove that it is a polynomial-time approximation scheme (PTAS).


Euclidean space Weighted 2-clustering Quadratic variation NP-hardness Approximation algorithm PTAS 


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Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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