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Diskretn. Anal. Issled. Oper.:

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Diskretn. Anal. Issled. Oper., 2011, Volume 18, Number 4, Pages 17–48 (Mi da658)  

This article is cited in 10 scientific papers (total in 10 papers)

Polynomial algorithm with approximation ratio $7/9$ for maximum 2-PSP

A. N. Glebovab, D. Zh. Zambalayevaa

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

Abstract: We study a 2-peripatetic salesman problem on maximum which consists in finding two edge-disjoint Hamiltonian cycles of maximum total weight in a complete undirected graph. We present a cubic time approximation algorithm for this problem with guaranteed ratio $7/9$, the best known for today. Ill. 5, bibliogr. 14.

Keywords: traveling salesman problem, 2-peripatetic salesman problem, polynomial algorithm, guaranteed approximation ratio.

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English version:
Journal of Applied and Industrial Mathematics, 2012, 6:1, 69–89

Bibliographic databases:

UDC: 519.8
Received: 25.01.2011
Revised: 06.05.2011

Citation: A. N. Glebov, D. Zh. Zambalayeva, “Polynomial algorithm with approximation ratio $7/9$ for maximum 2-PSP”, Diskretn. Anal. Issled. Oper., 18:4 (2011), 17–48; J. Appl. Industr. Math., 6:1 (2012), 69–89

Citation in format AMSBIB
\by A.~N.~Glebov, D.~Zh.~Zambalayeva
\paper Polynomial algorithm with approximation ratio $7/9$ for maximum 2-PSP
\jour Diskretn. Anal. Issled. Oper.
\yr 2011
\vol 18
\issue 4
\pages 17--48
\jour J. Appl. Industr. Math.
\yr 2012
\vol 6
\issue 1
\pages 69--89

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    This publication is cited in the following articles:
    1. E. Kh. Gimadi, E. V. Ivonina, “Approximation algorithms for maximum-weight problem of two-peripatetic salesmen”, J. Appl. Industr. Math., 6:3 (2012), 295–305  mathnet  crossref  mathscinet
    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. O. Yu. Tsidulko, “On solvability of the axial $8$-index assignment problem on one-cycle permutations”, J. Appl. Industr. Math., 8:1 (2014), 115–126  mathnet  crossref  mathscinet  isi
    4. 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”, J. Appl. Industr. Math., 8:2 (2014), 208–217  mathnet  crossref  mathscinet  isi
    5. A. N. Glebov, D. Zh. Zambalaeva, A. A. Skretneva, “$2/3$-approximation algorithm for the maximization version of the asymmetric two peripatetic salesman problem”, J. Appl. Industr. Math., 9:1 (2015), 61–67  mathnet  crossref  mathscinet
    6. 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
    7. Gimadi E.Kh. Glebov A.N. Skretneva A.A. Tsidulko O.Yu. Zambalaeva D.Zh., “Combinatorial Algorithms With Performance Guarantees For Finding Several Hamiltonian Circuits in a Complete Directed Weighted Graph”, Discrete Appl. Math., 196:SI (2015), 54–61  crossref  mathscinet  zmath  isi  elib  scopus
    8. 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
    9. Gimadi E.Kh. Tsidulko O.Yu., “Approximation Algorithms For the Maximum M-Peripatetic Salesman Problem”, Analysis of Images, Social Networks and Texts, Aist 2017, Lecture Notes in Computer Science, 10716, ed. VanDerAalst W. Ignatov D. Khachay M. Kuznetsov S. Lempitsky V. Lomazova I. Loukachevitch N. Napoli A. Panchenko A. Pardalos P. Savchenko A. Wasserman S., Springer International Publishing Ag, 2018, 304–312  crossref  mathscinet  isi  scopus
    10. A. N. Glebov, S. G. Toktokhoeva, “A polynomial $3/5$-approximate algorithm for the asymmetric maximization version of $3$-PSP”, J. Appl. Industr. Math., 13:2 (2019), 219–238  mathnet  crossref  crossref
  • Дискретный анализ и исследование операций
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