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Diskretn. Anal. Issled. Oper., 2017, Volume 24, Number 4, Pages 111–129 (Mi da885)  

This article is cited in 2 scientific papers (total in 2 papers)

An exact algorithm for finding a vector subset with the longest sum

V. V. Shenmaier

Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia

Abstract: 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, polynomial-time algorithm, optimal solution.

Funding Agency Grant Number
Russian Science Foundation 16-11-10041


DOI: https://doi.org/10.17377/daio.2017.24.541

Full text: PDF file (396 kB)
References: PDF file   HTML file

English version:
Journal of Applied and Industrial Mathematics, 2017, 11:4, 584–593

UDC: 519.16
Received: 22.05.2016
Revised: 10.05.2017

Citation: V. V. Shenmaier, “An exact algorithm for finding a vector subset with the longest sum”, Diskretn. Anal. Issled. Oper., 24:4 (2017), 111–129; J. Appl. Industr. Math., 11:4 (2017), 584–593

Citation in format AMSBIB
\Bibitem{She17}
\by V.~V.~Shenmaier
\paper An exact algorithm for finding a~vector subset with the longest sum
\jour Diskretn. Anal. Issled. Oper.
\yr 2017
\vol 24
\issue 4
\pages 111--129
\mathnet{http://mi.mathnet.ru/da885}
\crossref{https://doi.org/10.17377/daio.2017.24.541}
\elib{http://elibrary.ru/item.asp?id=30551370}
\transl
\jour J. Appl. Industr. Math.
\yr 2017
\vol 11
\issue 4
\pages 584--593
\crossref{https://doi.org/10.1134/S1990478917040160}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85036473903}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Shenmaier, “Approximability of the problem of finding a vector subset with the longest sum”, J. Appl. Industr. Math., 12:4 (2018), 749–758  mathnet  crossref  crossref  elib
    2. V. V. Shenmaier, “Complexity and approximation of finding the longest vector sum”, Comput. Math. Math. Phys., 58:6 (2018), 850–857  mathnet  crossref  crossref  isi  elib
  • Дискретный анализ и исследование операций
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