Реферат: 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.

Библиографическая ссылка: Kel’manov A.V. , Mikhailova L.V. , Khamidullin S.A. , Khandeev V.I.
Approximation algorithm for the problem of partitioning a sequence into clusters
Computational Mathematics and Mathematical Physics. 2017. V.57. N8. P.1376-1383. DOI: 10.1134/s0965542517080085 WOS Scopus OpenAlex

Оригинальная: Кельманов А.В. , Михайлова Л.В. , Хамидуллин С.А. , Хандеев В.И.
ПРИБЛИЖЕННЫЙ АЛГОРИТМ ДЛЯ ЗАДАЧИ РАЗБИЕНИЯ ПОСЛЕДОВАТЕЛЬНОСТИ НА КЛАСТЕРЫ
Журнал вычислительной математики и математической физики. 2017. Т.57. №8. С.1392-1400. DOI: 10.7868/s0044466917080087 РИНЦ OpenAlex

Идентификаторы БД:

Web of science:	WOS:000408956800011
Scopus:	2-s2.0-85028688948
OpenAlex:	W2751508009

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БД	Цитирований
OpenAlex	1

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