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Diskretn. Anal. Issled. Oper., 2014, Volume 21, Number 1, Pages 15–29 (Mi da757)  

This article is cited in 5 scientific papers (total in 5 papers)

The probabilistic analysis of an algorithm for solving the $m$-planar $3$-dimensional assignment problem on one-cycle permutations

E. Kh. Gimadiab, Yu. V. Glazkovb, O. Yu. Tsidulkob

a Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia
b Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia

Abstract: We study the $m$-planar $3$-dimensional assignment problem on one-cycle permutations. In other words, it is the $m$-peripatetic salesman problem ($m$-PSP) with different weight functions for each salesman. The problem is NP-hard for $m\ge1$. We introduce a polynomial approximation algorithm suggested for $1<m<n/4$ with time complexity $O(mn^2)$. The performance ratios of the algorithm are established for input data (elements of $(m\times n\times n)$-matrix) which are assumed to be independent and identically distributed random variables on $[a_n,b_n]$, where $0<a_n<b_n$. If the distribution is uniform or dominates the uniform distribution, conditions on $a_n,b_n$ and $m$ are obtained for the asymptotic optimality of the algorithm. Ill. 1, bibliogr. 26.

Keywords: $m$-planar $3$-dimensional assignment problem, one-cycle permutations, $m$-PSP with different weight functions, polynomial approximation algorithm, asymptotic optimality.

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English version:
Journal of Applied and Industrial Mathematics, 2014, 8:2, 208–217

Bibliographic databases:

UDC: 519.8
Received: 19.12.2012
Revised: 29.03.2013

Citation: 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”, Diskretn. Anal. Issled. Oper., 21:1 (2014), 15–29; J. Appl. Industr. Math., 8:2 (2014), 208–217

Citation in format AMSBIB
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\by E.~Kh.~Gimadi, Yu.~V.~Glazkov, O.~Yu.~Tsidulko
\paper The probabilistic analysis of an algorithm for solving the $m$-planar $3$-dimensional assignment problem on one-cycle permutations
\jour Diskretn. Anal. Issled. Oper.
\yr 2014
\vol 21
\issue 1
\pages 15--29
\mathnet{http://mi.mathnet.ru/da757}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3288378}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 2
\pages 208--217
\crossref{https://doi.org/10.1134/S1990478914020070}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902148101}


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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. E. Kh. Gimadi, A. M. Istomin, I. A. Rykov, O. Yu. Tsidulko, “Probabilistic analysis of an approximation algorithm for the $m$-peripatetic salesman problem on random instances unbounded from above”, Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 77–87  mathnet  crossref  mathscinet  isi  elib
    2. 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
    3. E. Kh. Gimadi, O. Yu. Tsidulko, “An asymptotically optimal algorithm for the $m$-peripatetic salesman problem on random inputs with discrete distribution”, J. Appl. Industr. Math., 11:3 (2017), 354–361  mathnet  crossref  crossref  elib
    4. E. Kh. Gimadi, O. Yu. Tsidulko, “Approximation algorithms for the maximum $m$-Peripatetic Salesman 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, 304–312  crossref  mathscinet  isi  scopus
    5. M. Khachay, K. Neznakhina, “Polynomial time solvable subclass of the Generalized Traveling Salesman Problem on Grid Clusters”, 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, 346–355  crossref  isi  scopus
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