A fully polynomial-time approximation scheme for a sequence 2-cluster partitioning problem
| Autor: | Alexander Kel'manov, Sergey A. Khamidullin, V. I. Khandeev |
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| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Euclidean space Applied Mathematics Space dimension Centroid 02 engineering and technology 01 natural sciences Industrial and Manufacturing Engineering Polynomial-time approximation scheme Finite sequence 010101 applied mathematics Combinatorics 020303 mechanical engineering & transports 0203 mechanical engineering Bounded function Cluster (physics) Partition (number theory) 0101 mathematics Mathematics |
| Zdroj: | Journal of Applied and Industrial Mathematics. 10:209-219 |
| ISSN: | 1990-4797 1990-4789 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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