Geodesic
An exact algorithm for finding a~vector subset with the longest sum
Diskretnyj analiz i issledovanie operacij, Tome 24 (2017) no. 4, pp. 111-129

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We consider the problem: Given a set of $n$ vectors in the $d$-dimensional Euclidean space, find a subset maximizing the length of the sum vector. We propose an algorithm that finds an optimal solution to this problem in time $O(n^{d-1}(d+\log n))$. In particular, if the input vectors lie in a plane then the problem is solvable in almost linear time. Illustr. 2, bibliogr. 14.
Keywords: sum vector, search for a vector subset, Euclidean space
Mots-clés : polynomial-time algorithm, optimal solution. 
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     author = {V. V. Shenmaier},
     title = {An exact algorithm for finding a~vector subset with the longest sum},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {111--129},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2017_24_4_a7/}
}
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V. V. Shenmaier. An exact algorithm for finding a~vector subset with the longest sum. Diskretnyj analiz i issledovanie operacij, Tome 24 (2017) no. 4, pp. 111-129. http://geodesic.mathdoc.fr/item/DA_2017_24_4_a7/