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An exact algorithm for finding a vector subset with the longest sum
Authors:V V Shenmaier
Institution:1.Sobolev Institute of Mathematics,Novosibirsk,Russia
Abstract:We consider the problem: Given a set of n vectors in the d-dimensional Euclidean space, find a subsetmaximizing the length of the sum vector.We propose an algorithm that finds an optimal solution to this problem in time O(nd?1(d + logn)). In particular, if the input vectors lie in a plane then the problem is solvable in almost linear time.
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