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Diskretn. Anal. Issled. Oper., 2009, Volume 16, Number 4, Pages 3–20 (Mi da576)  

This article is cited in 4 scientific papers (total in 4 papers)

A 2-approximation algorithm for the metric 2-peripatetic salesman problem

A. A. Ageevab, A. V. Pyatkinab

a S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: In the $m$-peripatetic traveling salesman problem, given an $n$-vertex complete undirected edge-weighted graph, it is required to find $m$ edge disjoint Hamiltonian cycles of minimum total weight. The problem was introduced by Krarup (1974) and has network design and scheduling applications. It is known that 2-PSP is NP-hard even in the metric case and does not admit any constant-factor approximation in the general case. Baburin, Gimadi, and Korkishko (2004) designed a $(9/4+\varepsilon)$-approximation algorithm for the metric case of 2-PSP, based on solving the traveling salesman problem. In the paper we present an improved 2-approximation algorithm with running time $O(n^2\log n)$ for the metric 2-PSP. Our algorithm exploits the fact that the problem of finding two edge disjoint spanning trees of minimum total weight is polynomially solvable. Il. 5, bibl. 12.

Keywords: approximation algorithm, Hamiltonian cycle, spanning tree, traveling salesman problem.

Full text: PDF file (335 kB)
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Bibliographic databases:

UDC: 519.178
Received: 21.02.2009
Revised: 12.05.2009

Citation: A. A. Ageev, A. V. Pyatkin, “A 2-approximation algorithm for the metric 2-peripatetic salesman problem”, Diskretn. Anal. Issled. Oper., 16:4 (2009), 3–20

Citation in format AMSBIB
\Bibitem{AgePya09}
\by A.~A.~Ageev, A.~V.~Pyatkin
\paper A 2-approximation algorithm for the metric 2-peripatetic salesman problem
\jour Diskretn. Anal. Issled. Oper.
\yr 2009
\vol 16
\issue 4
\pages 3--20
\mathnet{http://mi.mathnet.ru/da576}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2589404}
\zmath{https://zbmath.org/?q=an:1249.90296}


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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. E. Baburin, E. Kh. Gimadi, “On the asymptotic accuracy of an algorithm for solving the $m$-PSP maximum problem in a multidimensional Euclidean space”, Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S1–S13  mathnet  crossref  isi  elib
    2. E. Kh. Gimadi, A. M. Istomin, I. A. Rykov, “On $m$-capacitated peripatetic salesman problem”, J. Appl. Industr. Math., 8:1 (2014), 40–52  mathnet  crossref  mathscinet
    3. 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
    4. 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
  • Дискретный анализ и исследование операций
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