Volume 15, No 4, 2008, P. 30-43

UDC 519.8
E. Kh. Gimadi, Ju. V. Glazkov, I. A. Rykov
The vector subset problem with integer coordinates in euclidean space with the maximum sum

Abstract:
Two problems of selecting a subset of $m$ vectors with the maximum norm of sum from a set of $n$ vectors in Euclidean space $\mathbb R^k$ is considered. It is supposed that the coordinates of the vectors are integer. Using the dynamic programming technique new optimal algorithms are constructed. They have pseudopolynomial complexity, when the dimension $k$ of the vector space is fixed. New algorithms have certain advantages (with respect to earlier known algorithms): the vector subset problem can be solved faster, if $m<(k/2)^k$, and the time complexity is $k^{k-1}$ times less for the problem with an additional restriction on the order of vectors independently of $m$.
Bibl. 5.

Keywords: subset selection, Euclidian metric, time complexity, pseudopolynomial algorithm, dynamic programming.

Gimadi Edvard Khairutdinovich ¹
Glazkov Jurii Vladimirovich ¹
Rykov Ivan Aleksandrovich ¹
1. S. L. Sobolev Institute of Mathematics, SB RAS,
4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
e-mail: gimadi@math.nsc.ru, yg@ngs.ru, rykov@ledas.com