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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2014, Volume 14, Issue 3, Pages 3–18 (Mi vngu341)  

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

On 2-Capacitated Peripatetic Salesman Problem with Different Weight Functions

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

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

Abstract: We considered a particular case of a problem of finding $m$ Hamiltonian cycles with capacity restrictions on edges usage ($m$-Capacitated Peripatetic Salesman Problem, $m$-CPSP): the $2$-CPSP on minimum and maximum with edge weights from an integer segment $\{1,q\}$ with different weight functions. The edges capacities are independent identically distributed random variables, which is $2$ with probability $p$ and is $1$ with probability $(1-p)$. A polynomial algorithms for $2$-CPSP$_{\min}^d$ and $2$-CPSP$_{\max}^d$ with guarantee approximation ratio in average for all possible inputs was presented. In the case when edge weights are $1$ and $2$, the presented algorithms have approximation ratios $(19-5p)/12$ and $(25 + 7p)/36$ for the $2$-CPSP$_{\min}^d$ and the $2$-CPSP$_{\max}^d$ correspondingly.

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

Full text: PDF file (307 kB)
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UDC: 519.8
Received: 16.12.2013

Citation: E. Kh. Gimadi, A. M. Istomin, I. A. Rykov, “On 2-Capacitated Peripatetic Salesman Problem with Different Weight Functions”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 14:3 (2014), 3–18

Citation in format AMSBIB
\Bibitem{GimIstRyk14}
\by E.~Kh.~Gimadi, A.~M.~Istomin, I.~A.~Rykov
\paper On 2-Capacitated Peripatetic Salesman Problem with Different Weight Functions
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2014
\vol 14
\issue 3
\pages 3--18
\mathnet{http://mi.mathnet.ru/vngu341}


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    This publication is cited in the following articles:
    1. V. M. Nedelko, “K voprosu ob effektivnosti bustinga v zadache klassifikatsii”, Vestn. NGU. Ser. matem., mekh., inform., 15:2 (2015), 72–89  mathnet  crossref
  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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