# Approximation algorithm for the problem of partitioning a sequence into clusters

A. V. Kel’manov, L. V. Mikhailova, S. A. Khamidullin, V. I. Khandeev

Результат исследования: Научные публикации в периодических изданияхстатья

### Аннотация

We consider the problem of partitioning a finite sequence of Euclidean points into a given number of clusters (subsequences) using the criterion of the minimal sum (over all clusters) of intercluster sums of squared distances from the elements of the clusters to their centers. It is assumed that the center of one of the desired clusters is at the origin, while the center of each of the other clusters is unknown and determined as the mean value over all elements in this cluster. Additionally, the partition obeys two structural constraints on the indices of sequence elements contained in the clusters with unknown centers: (1) the concatenation of the indices of elements in these clusters is an increasing sequence, and (2) the difference between an index and the preceding one is bounded above and below by prescribed constants. It is shown that this problem is strongly NP-hard. A 2-approximation algorithm is constructed that is polynomial-time for a fixed number of clusters.

Язык оригинала английский 1376-1383 8 Computational Mathematics and Mathematical Physics 57 8 https://doi.org/10.1134/S0965542517080085 Опубликовано - 1 авг 2017