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Diskretn. Anal. Issled. Oper., 2014, Volume 21, Number 4, Pages 3–11 (Mi da780)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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.

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English version:
Journal of Applied and Industrial Mathematics, 2014, 8:4, 453–457

Bibliographic databases:

UDC: 519.2+621.391
Received: 03.12.2013
Revised: 10.02.2014

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://www.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 articles:
    1. A. V. Kel'manov, A. V. Pyatkin, “On the complexity of some quadratic Euclidean 2-clustering problems”, Comput. Math. Math. Phys., 56:3 (2016), 491–497  mathnet  crossref  elib
  • Дискретный анализ и исследование операций
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