A fully polynomial-time approximation scheme for a sequence 2-cluster partitioning problem

被引：0

作者：

Kel’manov A.V. ^{[1
,2
]}

Khamidullin S.A. ^{[1
]}

Khandeev V.I. ^{[1
]}

机构：

[1] Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk

[2] Novosibirsk State University, ul. Pirogova 2, Novosibirsk

来源：

Journal of Applied and Industrial Mathematics | 2016年 / 10卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

Euclidean space; FPTAS; minimum sum-of-squared distances; NPhardness; partitioning; sequence;

D O I：

10.1134/S199047891602006X

中图分类号：

学科分类号：

摘要：

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. © 2016, Pleiades Publishing, Ltd.

引用

页码：209 / 219

页数：10

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