### Abstract

We consider a problem of finding a subset of the smallest size in the given set of vectors such that the norm of sum vector is greater or equal to some given value. We show that the problem can be solved optimally with the same complexity as the problem of finding the subset of given cardinality with minimum norm of sum vector.

Original language | English |
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Title of host publication | Optimization Problems and Their Applications - 7th International Conference, OPTA 2018, Revised Selected Papers |

Publisher | Springer-Verlag GmbH and Co. KG |

Pages | 131-136 |

Number of pages | 6 |

ISBN (Print) | 9783319937991 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

Event | 7th International Conference on Optimization Problems and Their Applications, OPTA 2018 - Omsk, Russian Federation Duration: 8 Jun 2018 → 14 Jun 2018 |

### Publication series

Name | Communications in Computer and Information Science |
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Volume | 871 |

ISSN (Print) | 1865-0929 |

### Conference

Conference | 7th International Conference on Optimization Problems and Their Applications, OPTA 2018 |
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Country | Russian Federation |

City | Omsk |

Period | 08.06.2018 → 14.06.2018 |

### Keywords

- Euclidean space
- Exact algorithm
- Sum vector
- Vector subset

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## Cite this

Gimadi, E. K., Rykov, I. A., & Shamardin, Y. V. (2018). On vector summation problem in the euclidean space. In

*Optimization Problems and Their Applications - 7th International Conference, OPTA 2018, Revised Selected Papers*(pp. 131-136). (Communications in Computer and Information Science; Vol. 871). Springer-Verlag GmbH and Co. KG. https://doi.org/10.1007/978-3-319-93800-4_11