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Diskretn. Anal. Issled. Oper., 2016, Volume 23, Number 4, Pages 102–115 (Mi da859)  

This article is cited in 8 scientific papers (total in 8 papers)

Solving some vector subset problems by Voronoi diagrams

V. V. Shenmaier

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

Abstract: We propose a general approach to solving some vector subset problems in a Euclidean space that is based on higher-order Voronoi diagrams. In the case of a fixed space dimension, this approach allows us to find optimal solutions to these problems in polynomial time which is better than the runtime of available algorithms. Ill. 1, bibliogr. 16.

Keywords: computational geometry, vector subset problem, Euclidean space, Voronoi diagram, polynomial-time algorithm.

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


DOI: https://doi.org/10.17377/daio.2016.23.526

Full text: PDF file (286 kB)
References: PDF file   HTML file

English version:
Journal of Applied and Industrial Mathematics, 2016, 10:4, 560–566

Bibliographic databases:

UDC: 519.176
Received: 20.05.2016
Revised: 15.06.2016

Citation: V. V. Shenmaier, “Solving some vector subset problems by Voronoi diagrams”, Diskretn. Anal. Issled. Oper., 23:4 (2016), 102–115; J. Appl. Industr. Math., 10:4 (2016), 560–566

Citation in format AMSBIB
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\by V.~V.~Shenmaier
\paper Solving some vector subset problems by Voronoi diagrams
\jour Diskretn. Anal. Issled. Oper.
\yr 2016
\vol 23
\issue 4
\pages 102--115
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3581886}
\elib{http://elibrary.ru/item.asp?id=27349045}
\transl
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
\issue 4
\pages 560--566
\crossref{https://doi.org/10.1134/S199047891604013X}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84996487016}


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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. A. V. Kelmanov, A. V. Motkova, V. V. Shenmaier, “Priblizhennaya skhema dlya zadachi vzveshennoi 2-klasterizatsii s fiksirovannym tsentrom odnogo klastera”, Tr. IMM UrO RAN, 23, no. 3, 2017, 159–170  mathnet  crossref  elib
    2. V. V. Shenmaier, “An exact algorithm for finding a vector subset with the longest sum”, J. Appl. Industr. Math., 11:4 (2017), 584–593  mathnet  crossref  crossref  elib
    3. A. Ageev, A. Kel'manov, A. Pyatkin, S. Khamidullin, V. Shenmaier, “1/2-approximation polynomial-time algorithm for a problem of searching a subset”, 2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON), IEEE, 2017, 8–12  crossref  isi
    4. A. Kel'manov, “Efficient approximation algorithms for some NP-hard problems of partitioning a set and a sequence”, 2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON), IEEE, 2017, 87–90  crossref  isi
    5. A. Kel'manov, V. Khandeev, “Some algorithms with guaranteed accuracy for 2-clustering problems with given center of one cluster”, 2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON), IEEE, 2017, 91–93  crossref  isi
    6. 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
    7. 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
    8. A. Kel'manov, A. Motkova, V. Shenmaier, “An approximation scheme for a weighted two-cluster partition problem”, Analysis of Images, Social Networks and Texts, AIST 2017, Lecture Notes in Computer Science, 10716, eds. W. van der Aalst, D. Ignatov, M. Khachay, S. Kuznetsov, V. Lempitsky, I. Lomazova, N. Loukachevitch, A. Napoli, A. Panchenko, P. Pardalos, A. Savchenko, S. Wasserman, Springer, 2018, 323–333  crossref  isi  scopus
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