A fully polynomial-time approximation scheme for a sequence 2-cluster partitioning problem
- Authors: Kel’manov A.V.1,2, Khamidullin S.A.1, Khandeev V.I.1
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Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Issue: Vol 10, No 2 (2016)
- Pages: 209-219
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/212331
- DOI: https://doi.org/10.1134/S199047891602006X
- ID: 212331
Cite item
Abstract
We consider a strongly NP-hard problem of partitioning a finite sequence of points in Euclidean space into the two clustersminimizing the sum over both clusters of intra-cluster sums of squared distances from the clusters elements to their centers. The sizes of the clusters are fixed. The centroid of the first cluster is defined as the mean value of all vectors in the cluster, and the center of the second cluster is given in advance and equals 0. Additionally, the partition must satisfy the restriction that for all vectors in the first cluster the difference between the indices of two consequent points from this cluster is bounded from below and above by some given constants.We present a fully polynomial-time approximation scheme for the case of fixed space dimension.
About the authors
A. V. Kel’manov
Sobolev Institute of Mathematics; Novosibirsk State University
Author for correspondence.
Email: kelm@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090
S. A. Khamidullin
Sobolev Institute of Mathematics
Email: kelm@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090
V. I. Khandeev
Sobolev Institute of Mathematics
Email: kelm@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090