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Diskretnyi Analiz i Issledovanie Operatsii, 2014, Volume 21, Issue 4, Pages 3–11 (Mi da780)  
This article is cited in 5 scientific papers (total in 5 papers)

Complexity of the Euclidean max cut problem

A. A. Ageeva, A. V. Kel'manovab, A. V. Pyatkinab

a S. L. Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
b Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia
Full-text PDF (222 kB) Citations (5)
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Abstract: We consider the following problem: given a complete edge-weighted undirected graph whose vertices are points of a $q$-dimensional space, find a cut of maximum total weight. Two special cases are analyzed where the edge weights are equal to (i) the Euclidean distances between points representing the vertices, (ii) the squares of these distances. We prove that both cases of the problem are strongly NP-hard do no permit FPTAS unless $\mathrm{P\neq NP}$. Bibliogr. 17.
Keywords: graph, cut, Euclidean space, NP-hard problem.
Received: 03.12.2013
Revised: 10.02.2014
English version:
Journal of Applied and Industrial Mathematics, 2014, Volume 8, Issue 4, Pages 453–457
DOI: https://doi.org/10.1134/S1990478914040012
Bibliographic databases:
Document Type: Article
UDC: 519.2+621.391
Language: Russian
Citation: A. A. Ageev, A. V. Kel'manov, A. V. Pyatkin, “Complexity of the Euclidean max cut problem”, Diskretn. Anal. Issled. Oper., 21:4 (2014), 3–11; J. Appl. Industr. Math., 8:4 (2014), 453–457
Citation in format AMSBIB
\Bibitem{AgeKelPya14}
\by A.~A.~Ageev, A.~V.~Kel'manov, A.~V.~Pyatkin
\paper Complexity of the Euclidean max cut problem
\jour Diskretn. Anal. Issled. Oper.
\yr 2014
\vol 21
\issue 4
\pages 3--11
\mathnet{http://mi.mathnet.ru/da780}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3289216}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 4
\pages 453--457
\crossref{https://doi.org/10.1134/S1990478914040012}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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