Geodesic
Approximation algorithm for one problem of partitioning a~sequence
Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 1, pp. 53-66

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We consider one NP-hard problem of partitioning of a finite Euclidean vectors sequence into two clusters minimizing the sum of squared distances from the clusters elements to their centers. The cardinalities of the clusters are fixed. The center of the first cluster is defined as the mean value of all vectors in a cluster. The center of the second cluster is given in advance and is equal to 0. Additionally, the partition must satisfy the restriction that for all vectors that are in the first cluster the difference between the indices of two consequent vectors from this cluster is bounded from below and above by some constants. An effective $2$-approximation algorithm for the problem is presented. Bibliogr. 9.
Keywords: Euclidean vectors sequence, сlusterization, minimum sum-of-squared distances, NP-hardness, effective $2$-approximation algorithm. 
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     author = {A. V. Kelmanov and S. A. Khamidullin},
     title = {Approximation algorithm for one problem of partitioning a~sequence},
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A. V. Kelmanov; S. A. Khamidullin. Approximation algorithm for one problem of partitioning a~sequence. Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 1, pp. 53-66. http://geodesic.mathdoc.fr/item/DA_2014_21_1_a4/