A 2-approximate algorithm to solve one problem of the family of disjoint vector subsets
Consideration was given to the problem of seeking a family of disjoint subsets of given cardinalities in a finite set of Euclidean space vectors. The minimal sum of the squared distances from the subset elements to their centers was used as the search criterion. The subset centers are optimizable va...
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| Veröffentlicht in: | Automation and remote control 2014-04, Vol.75 (4), p.595-606 |
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| container_title | Automation and remote control |
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| creator | Galashov, A. E. Kel’manov, A. V. |
| description | Consideration was given to the problem of seeking a family of disjoint subsets of given cardinalities in a finite set of Euclidean space vectors. The minimal sum of the squared distances from the subset elements to their centers was used as the search criterion. The subset centers are optimizable variables defined as the mean values over the elements of the required subsets. The problem was shown to be NP-hard in the strong sense. To solve it, a 2-approximate algorithm was proposed which is polynomial for a fixed number of the desired subsets. |
| doi_str_mv | 10.1134/S0005117914040018 |
| format | Article |
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| ispartof | Automation and remote control, 2014-04, Vol.75 (4), p.595-606 |
| issn | 0005-1179 1608-3032 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1551041558 |
| source | SpringerNature Journals |
| subjects | Algorithms Automation CAE) and Design Calculus of Variations and Optimal Control Optimization Computer-Aided Engineering (CAD Control Criteria Mathematical analysis Mathematical Programming Problems Mathematics Mathematics and Statistics Mechanical Engineering Mechatronics Polynomials Remote control Robotics Searching Systems Theory Vectors (mathematics) |
| title | A 2-approximate algorithm to solve one problem of the family of disjoint vector subsets |
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