Geodesic
The vector subset problem with integer coordinates in Euclidean space with the maximum sum
Diskretnyj analiz i issledovanie operacij, Tome 15 (2008) no. 4, pp. 30-43

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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, dynamic programming.
Mots-clés : pseudopolynomial algorithm 
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     author = {E. Kh. Gimadi and Yu. V. Glazkov and I. A. Rykov},
     title = {The vector subset problem with integer coordinates in {Euclidean} space with the maximum sum},
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     pages = {30--43},
     publisher = {mathdoc},
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     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2008_15_4_a2/}
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E. Kh. Gimadi; Yu. V. Glazkov; I. A. Rykov. The vector subset problem with integer coordinates in Euclidean space with the maximum sum. Diskretnyj analiz i issledovanie operacij, Tome 15 (2008) no. 4, pp. 30-43. http://geodesic.mathdoc.fr/item/DA_2008_15_4_a2/