A parameterized approximation algorithm for the mixed and windy Capacitated Arc Routing Problem: theory and experiments

We prove that any polynomial-time \(\alpha(n)\)-approximation algorithm for the \(n\)-vertex metric asymmetric Traveling Salesperson Problem yields a polynomial-time \(O(\alpha(C))\)-approximation algorithm for the mixed and windy Capacitated Arc Routing Problem, where \(C\) is the number of weakly...

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Bibliographic Details
Published in:arXiv.org
Main Authors: René van Bevern, Komusiewicz, Christian, Sorge, Manuel
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 16.10.2016
Subjects:
Algorithms
Approximation
Benchmarks
Computer simulation
Graph theory
Mathematical analysis
Polynomials
Production scheduling
ISSN:2331-8422
Online Access:Get full text
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Summary:We prove that any polynomial-time \(\alpha(n)\)-approximation algorithm for the \(n\)-vertex metric asymmetric Traveling Salesperson Problem yields a polynomial-time \(O(\alpha(C))\)-approximation algorithm for the mixed and windy Capacitated Arc Routing Problem, where \(C\) is the number of weakly connected components in the subgraph induced by the positive-demand arcs---a small number in many applications. In conjunction with known results, we obtain constant-factor approximations for \(C\in O(\log n)\) and \(O(\log C/\log\log C)\)-approximations in general. Experiments show that our algorithm, together with several heuristic enhancements, outperforms many previous polynomial-time heuristics. Finally, since the solution quality achievable in polynomial time appears to mainly depend on \(C\) and since \(C=1\) in almost all benchmark instances, we propose the Ob benchmark set, simulating cities that are divided into several components by a river.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
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ISSN:2331-8422
DOI:10.48550/arxiv.1506.05620