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Diskretn. Anal. Issled. Oper., Ser. 2, 2006, Volume 13, Number 1, Pages 10–26 (Mi da15)  

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

An asymptotically exact algorithm for one modification of planar three-index assignment

E. Kh. Gimadi, Yu. V. Glazkov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: An $m$-layer three-index assignment problem is considered which is a modification of the classical planar three-index assignment problem. This problem is NP-hard for $m\geqslant2$. An approximate algorithm, solving this problem for $1<m<n/2$, is suggested. The bounds on its quality are proved in the case when the input data (the elements of an $m\times n\times n$ matrix) are independent identically distributed random variables whose values lie in the interval $[a_n,b_n]$, where $b_n>a_n>0$. The time complexity of the algorithm is $O(mn^2+m^{7/2})$. It is shown that in the case of a uniform distribution (and also a distribution of minorized type) the algorithm is asymptotically exact if $m=\Theta(n^{1-\theta})$ and $b_n/a_n=o(n^\theta)$ for every constant $\theta$, $0<\theta<1$.

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English version:
Journal of Applied and Industrial Mathematics, 2007, 1:4, 442–452

Bibliographic databases:


Citation: E. Kh. Gimadi, Yu. V. Glazkov, “An asymptotically exact algorithm for one modification of planar three-index assignment”, Diskretn. Anal. Issled. Oper., Ser. 2, 13:1 (2006), 10–26; J. Appl. Industr. Math., 1:4 (2007), 442–452

Citation in format AMSBIB
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\by E.~Kh.~Gimadi, Yu.~V.~Glazkov
\paper An asymptotically exact algorithm for one modification of planar three-index assignment
\jour Diskretn. Anal. Issled. Oper., Ser.~2
\yr 2006
\vol 13
\issue 1
\pages 10--26
\mathnet{http://mi.mathnet.ru/da15}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2288949}
\zmath{https://zbmath.org/?q=an:1249.90221}
\transl
\jour J. Appl. Industr. Math.
\yr 2007
\vol 1
\issue 4
\pages 442--452
\crossref{https://doi.org/10.1134/S1990478907040072}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-37249071814}


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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. Yokoya D., Duin C.W., Yamada T., “A reduction approach to the repeated assignment problem”, European J. Oper. Res., 210:2 (2011), 185–193  crossref  mathscinet  zmath  isi  elib  scopus
    2. L. G. Afraimovich, “Multi-index transport problems with decomposition structure”, Autom. Remote Control, 73:1 (2012), 118–133  mathnet  crossref  isi
    3. Afraimovich L.G., Katerov A.S., “Trekh- i chetyrekhindeksnye zadachi s vlozhennoi strukturoi”, Vestnik nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2012, 163–169  elib
    4. L. G. Afraimovich, “Multiindex transportation problems with $2$-embedded structure”, Autom. Remote Control, 74:1 (2013), 90–104  mathnet  crossref  isi
    5. E. Kh. Gimadi, Yu. V. Glazkov, O. Yu. Tsidulko, “The probabilistic analysis of an algorithm for solving the $m$-planar $3$-dimensional assignment problem on one-cycle permutations”, J. Appl. Industr. Math., 8:2 (2014), 208–217  mathnet  crossref  mathscinet  isi
    6. L. G. Afraimovich, “A heuristic method for solving integer-valued decompositional multiindex problems”, Autom. Remote Control, 75:8 (2014), 1357–1368  mathnet  crossref  isi
    7. E. Kh. Gimadi, E. Yu. Shin, “Probabilistic analysis of an algorithm for the minimum spanning tree problem with diameter bounded from below”, J. Appl. Industr. Math., 9:4 (2015), 480–488  mathnet  crossref  crossref  mathscinet  elib
    8. Gimadi E.Kh., “Efficient Algorithms With Performance Guarantees For Some Problems of Finding Several Discrete Disjoint Subgraphs in Complete Weighted Graph”, Appl. Math. Comput., 255 (2015), 84–91  crossref  mathscinet  zmath  isi  elib  scopus
  • Дискретный анализ и исследование операций
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