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Four-point conditions for the TSP: The complete complexity classification. / Deineko, Vladimir G.; Klinz, Bettina; Tiskin, Alexander; Woeginger, Gerhard J.

In: Discrete Optimization, Vol. 14, 01.11.2014, p. 147-159.

Research output: Contribution to journal › Article › peer-review

Harvard

Deineko, VG, Klinz, B, Tiskin, A & Woeginger, GJ 2014, 'Four-point conditions for the TSP: The complete complexity classification', Discrete Optimization, vol. 14, pp. 147-159. https://doi.org/10.1016/j.disopt.2014.09.003

APA

Deineko, V. G., Klinz, B., Tiskin, A., & Woeginger, G. J. (2014). Four-point conditions for the TSP: The complete complexity classification. Discrete Optimization, 14, 147-159. https://doi.org/10.1016/j.disopt.2014.09.003

Vancouver

Deineko VG, Klinz B, Tiskin A, Woeginger GJ. Four-point conditions for the TSP: The complete complexity classification. Discrete Optimization. 2014 Nov 1;14:147-159. https://doi.org/10.1016/j.disopt.2014.09.003

Author

Deineko, Vladimir G. ; Klinz, Bettina ; Tiskin, Alexander ; Woeginger, Gerhard J. / Four-point conditions for the TSP: The complete complexity classification. In: Discrete Optimization. 2014 ; Vol. 14. pp. 147-159.

BibTeX

@article{a3c18c500b7b40eda8c16ad699a1afa3,
title = "Four-point conditions for the TSP: The complete complexity classification",
abstract = "The combinatorial optimization literature contains a multitude of polynomially solvable special cases of the traveling salesman problem (TSP) which result from imposing certain combinatorial restrictions on the underlying distance matrices. Many of these special cases have the form of so-called four-point conditions: inequalities that involve the distances between four arbitrary cities. In this paper we classify all possible four-point conditions for the TSP with respect to computational complexity, and we determine for each of them whether the resulting special case of the TSP can be solved in polynomial time or whether it remains NP-hard.",
keywords = "Four-point condition, Polynomially solvable case, Traveling salesman problem",
author = "Deineko, {Vladimir G.} and Bettina Klinz and Alexander Tiskin and Woeginger, {Gerhard J.}",
year = "2014",
month = nov,
day = "1",
doi = "10.1016/j.disopt.2014.09.003",
language = "English",
volume = "14",
pages = "147--159",
journal = "Discrete Optimization",
issn = "1572-5286",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Four-point conditions for the TSP: The complete complexity classification

AU - Deineko, Vladimir G.

AU - Klinz, Bettina

AU - Tiskin, Alexander

AU - Woeginger, Gerhard J.

PY - 2014/11/1

Y1 - 2014/11/1

N2 - The combinatorial optimization literature contains a multitude of polynomially solvable special cases of the traveling salesman problem (TSP) which result from imposing certain combinatorial restrictions on the underlying distance matrices. Many of these special cases have the form of so-called four-point conditions: inequalities that involve the distances between four arbitrary cities. In this paper we classify all possible four-point conditions for the TSP with respect to computational complexity, and we determine for each of them whether the resulting special case of the TSP can be solved in polynomial time or whether it remains NP-hard.

AB - The combinatorial optimization literature contains a multitude of polynomially solvable special cases of the traveling salesman problem (TSP) which result from imposing certain combinatorial restrictions on the underlying distance matrices. Many of these special cases have the form of so-called four-point conditions: inequalities that involve the distances between four arbitrary cities. In this paper we classify all possible four-point conditions for the TSP with respect to computational complexity, and we determine for each of them whether the resulting special case of the TSP can be solved in polynomial time or whether it remains NP-hard.

KW - Four-point condition

KW - Polynomially solvable case

KW - Traveling salesman problem

UR - http://www.scopus.com/inward/record.url?scp=84939497913&partnerID=8YFLogxK

U2 - 10.1016/j.disopt.2014.09.003

DO - 10.1016/j.disopt.2014.09.003

M3 - Article

AN - SCOPUS:84939497913

VL - 14

SP - 147

EP - 159

JO - Discrete Optimization

JF - Discrete Optimization

SN - 1572-5286

ER -

ID: 127707464