Constant-factor approximations for Capacitated Arc Routing without triangle inequality

René Van Bevern; Sepp Hartung; André Nichterlein; Manuel Sorge

doi:10.1016/j.orl.2014.05.002

Constant-factor approximations for Capacitated Arc Routing without triangle inequality

René Van Bevern, Sepp Hartung, André Nichterlein, Manuel Sorge

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

14 Scopus citations

Abstract

Given an undirected graph with edge costs and edge demands, the Capacitated Arc Routing problem (CARP) asks for minimum-cost routes for equal-capacity vehicles so as to satisfy all demands. Constant-factor polynomial-time approximation algorithms were proposed for CARP with triangle inequality, while CARP was claimed to be NP-hard to approximate within any constant factor in general. Correcting this claim, we show that any factor α approximation for CARP with triangle inequality yields a factor α approximation for the general CARP.

Original language	English
Pages (from-to)	290-292
Number of pages	3
Journal	Operations Research Letters
Volume	42
Issue number	4
DOIs	https://doi.org/10.1016/j.orl.2014.05.002
State	Published - 1 Jan 2014
Externally published	Yes

Keywords

Chinese postman
NP-hard problem
Polynomial-time approximation
Rural postman
Vehicle routing

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2014.05.002

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abstract = "Given an undirected graph with edge costs and edge demands, the Capacitated Arc Routing problem (CARP) asks for minimum-cost routes for equal-capacity vehicles so as to satisfy all demands. Constant-factor polynomial-time approximation algorithms were proposed for CARP with triangle inequality, while CARP was claimed to be NP-hard to approximate within any constant factor in general. Correcting this claim, we show that any factor α approximation for CARP with triangle inequality yields a factor α approximation for the general CARP.",

keywords = "Chinese postman, NP-hard problem, Polynomial-time approximation, Rural postman, Vehicle routing",

author = "{Van Bevern}, Ren{\'e} and Sepp Hartung and Andr{\'e} Nichterlein and Manuel Sorge",

note = "Funding Information: Ren{\'e} van Bevern and Manuel Sorge acknowledge support of the Deutsche Forschungsgemeinschaft (DFG) , project DAPA ( NI 369/12 ).",

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AU - Van Bevern, René

AU - Hartung, Sepp

AU - Nichterlein, André

AU - Sorge, Manuel

N1 - Funding Information: René van Bevern and Manuel Sorge acknowledge support of the Deutsche Forschungsgemeinschaft (DFG) , project DAPA ( NI 369/12 ).

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Given an undirected graph with edge costs and edge demands, the Capacitated Arc Routing problem (CARP) asks for minimum-cost routes for equal-capacity vehicles so as to satisfy all demands. Constant-factor polynomial-time approximation algorithms were proposed for CARP with triangle inequality, while CARP was claimed to be NP-hard to approximate within any constant factor in general. Correcting this claim, we show that any factor α approximation for CARP with triangle inequality yields a factor α approximation for the general CARP.

AB - Given an undirected graph with edge costs and edge demands, the Capacitated Arc Routing problem (CARP) asks for minimum-cost routes for equal-capacity vehicles so as to satisfy all demands. Constant-factor polynomial-time approximation algorithms were proposed for CARP with triangle inequality, while CARP was claimed to be NP-hard to approximate within any constant factor in general. Correcting this claim, we show that any factor α approximation for CARP with triangle inequality yields a factor α approximation for the general CARP.

KW - Chinese postman

KW - NP-hard problem

KW - Polynomial-time approximation

KW - Rural postman

KW - Vehicle routing

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JF - Operations Research Letters

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ER -

Constant-factor approximations for Capacitated Arc Routing without triangle inequality

Abstract

Keywords

ASJC Scopus subject areas

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