The vector subset problem with integer coordinates in Euclidean space with the maximum sum

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.