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Diskretn. Anal. Issled. Oper., 2013, Volume 20, Number 5, Pages 13–30 (Mi da743)  

This article is cited in 2 scientific papers (total in 2 papers)

On $m$-capacitated peripatetic salesman problem

E. Kh. Gimadiab, A. M. Istomina, I. A. Rykovab

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

Abstract: We consider a particular case of the problem of finding $m$ Hamiltonian cycles with capacity restrictions on edges usage ($m$-Capacitated Peripatetic Salesman Problem, $m$-$\mathrm{CPSP}$): the $2$-CPSP on minimum and maximum with edge weights from an integer segment $\{1,q\}$. The edges capacities are independent identically distributed random variables which assume $2$ with probability $p$ and $1$ with probability $1-p$. Polynomial algorithms for $2$-$\mathrm{CPSP_{min}}$ and $2$-$\mathrm{CPSP_{max}}$ with guarantee approximation ratio in average for all possible inputs are presented. In the case when edge weights are $1$ and $2$, the presented algorithms have approximation ratio $(19-5p)/12$ and $(25+7p)/36$ for the $2$-$\mathrm{CPSP_{min}}$ and the $2$-$\mathrm{CPSP_{max}}$ correspondingly. Ill. 17, bibliogr. 20.

Keywords: travelling salesman problem, $m$-peripatetic salesman problem, approximation algorithm, edge-disjoint Hamiltonian cycle, guarantee approximation ratio.

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English version:
Journal of Applied and Industrial Mathematics, 2014, 8:1, 40–52

Bibliographic databases:

UDC: 519.8
Received: 27.12.2012
Revised: 10.06.2013

Citation: E. Kh. Gimadi, A. M. Istomin, I. A. Rykov, “On $m$-capacitated peripatetic salesman problem”, Diskretn. Anal. Issled. Oper., 20:5 (2013), 13–30; J. Appl. Industr. Math., 8:1 (2014), 40–52

Citation in format AMSBIB
\Bibitem{GimIstRyk13}
\by E.~Kh.~Gimadi, A.~M.~Istomin, I.~A.~Rykov
\paper On $m$-capacitated peripatetic salesman problem
\jour Diskretn. Anal. Issled. Oper.
\yr 2013
\vol 20
\issue 5
\pages 13--30
\mathnet{http://mi.mathnet.ru/da743}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184441}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 1
\pages 40--52
\crossref{https://doi.org/10.1134/S1990478914010050}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84894299351}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Istomin, “Veroyatnostnyi analiz odnoi zadachi marshrutizatsii”, Diskretn. analiz i issled. oper., 21:4 (2014), 42–53  mathnet  mathscinet
    2. E. Kh. Gimadi, A. M. Istomin, I. A. Rykov, “Zadacha o dvukh kommivoyazherakh s ogranicheniyami na propusknye sposobnosti reber grafa s razlichnymi vesovymi funktsiyami”, Vestn. NGU. Ser. matem., mekh., inform., 14:3 (2014), 3–18  mathnet
  • Дискретный анализ и исследование операций
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