EN|RU Volume 15, No 6, 2008, P. 11-19 UDC 519.8519.8519.8 E. Kh. Gimadi, A. V. Pyatkin, I. A. Rykov On polynomial solvability of some vector subset problems in euclidean space with fixed dimension Abstract: Problems of choosing vectors in the multidimensional Euclidean space $\mathbb R^k$ are considered. The maximum norm of sum or the averaged square of the norm are considered as the problem objective. We present combinatorial algorithms with time complexity $O(k^2n^{2k})$. Thereby it is shown that the considered problems are polynomially solvable for fixed dimension of space $\mathbb R^k$. Bibl. 6. Keywords: vector subset, Euclidean space, polynomial solvability. Gimadi Edward Khairutdinovich 1 Pyatkin Artem Valerievich 1 Rykov Ivan Alexandrovich 1 1. S. L. Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia e-mail: gimadi@math.nsc.ru, artem@math.nsc.ru, rykov@math.nsc.ru © Sobolev Institute of Mathematics, 2015