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On Minimizing Supermodular Functions on Hereditary Systems Read chapter Read first chapter

2018 | OriginalPaper | Chapter

On Vector Summation Problem in the Euclidean Space

Authors : Edward Kh. Gimadi, Ivan A. Rykov, Yury V. Shamardin

Published in: Optimization Problems and Their Applications

Publisher: Springer International Publishing

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Abstract

We consider a problem of finding a subset of the smallest size in the given set of vectors such that the norm of sum vector is greater or equal to some given value. We show that the problem can be solved optimally with the same complexity as the problem of finding the subset of given cardinality with minimum norm of sum vector.

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previous chapter An Approximation Polynomial Algorithm for a Problem of Searching for the Longest Subsequence in a Finite Sequence of Points in Euclidean Space
next chapter Fast Numerical Evaluation of Periodic Solutions for a Class of Nonlinear Systems and Its Applications for Parameter Estimation Problems
Literature
1.
Baburin, A., Pyatkin, A.: Polynomial algorithms for solving the vector sum problem. J. Appl. Industr. Math. 1(3), 268–272 (2007)CrossRef
2.
Baburin, A., Gimadi, E., Glebov, N., Pyatkin, A.: The problem of finding a subset of vectors with the maximum total weight. J. Appl. Industr. Math. 2(1), 32–38 (2008)MathSciNetCrossRef
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Gimadi, E., Kel’manov, A., Kel’manova, M., Khamidullin, S.: A posteriori detecting a quasiperiodic fragment in a numerical sequence. Pattern Recogn. Image Anal. 18(1), 30–42 (2008)CrossRef
4.
Gimadi, E., Pyatkin, A., Rykov, I.: On polynomial solvability of some problems of a vector subset choice in a euclidean space of fixed dimension. J. Appl. Industr. Math. 4(48), 48–53 (2010)CrossRef
5.
Gimadi, E., Rykov, I.: A randomized algorithm for finding a subset of vectors with the maximum euclidean norm of their sum. J. Appl. Industr. Math. 9(3), 351–357 (2015)CrossRef
6.
Pyatkin, A.: On the complexity of the maximum sum length vectors subset choice problem. J. Appl. Industr. Math. 4(4), 549–552 (2010)MathSciNetCrossRef
7.
Shenmaier, V.: Solving some vector subset problems by voronoi diagrams. J. Appl. Industr. Math. 10(4), 550–566 (2016)MathSciNetCrossRef
Metadata
Title
On Vector Summation Problem in the Euclidean Space
Authors
Edward Kh. Gimadi
Ivan A. Rykov
Yury V. Shamardin
Copyright Year
2018
Book
Optimization Problems and Their Applications

Print ISBN: 978-3-319-93799-1

Electronic ISBN: 978-3-319-93800-4

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-93800-4_11

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