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

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.

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Bibliographic databases:

UDC: 519.178
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
Related articles on Google Scholar: Russian articles, English articles

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
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
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
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
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