A parameterized approximation algorithm for the mixed and windy capacitated arc routing problem: Theory and experiments
We prove that any polynomial‐time α ( n ) ‐approximation algorithm for the n‐vertex metric asymmetric Traveling Salesperson Problem yields a polynomial‐time O ( α ( C ) ) ‐approximation algorithm for the mixed and windy Capacitated Arc Routing Problem, where C is the number of weakly connected compo...
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| Vydáno v: | Networks Ročník 70; číslo 3; s. 262 - 278 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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01.10.2017
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| ISSN: | 0028-3045, 1097-0037 |
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| Abstract | We prove that any polynomial‐time
α
(
n
)
‐approximation algorithm for the n‐vertex metric asymmetric Traveling Salesperson Problem yields a polynomial‐time
O
(
α
(
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
∈
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. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 262–278 2017 |
|---|---|
| AbstractList | 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 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. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 262-278 2017 We prove that any polynomial‐time α ( n ) ‐approximation algorithm for the n‐vertex metric asymmetric Traveling Salesperson Problem yields a polynomial‐time O ( α ( 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 ∈ 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. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 262–278 2017 We prove that any polynomial‐time ‐approximation algorithm for the n ‐vertex metric asymmetric Traveling Salesperson Problem yields a polynomial‐time ‐approximation algorithm for the mixed and windy Capacitated Arc Routing Problem, where 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 and ‐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. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 262–278 2017 |
| Author | Komusiewicz, Christian van Bevern, René Sorge, Manuel |
| Author_xml | – sequence: 1 givenname: René orcidid: 0000-0002-4805-218X surname: van Bevern fullname: van Bevern, René email: rvb@nsu.ru organization: Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences – sequence: 2 givenname: Christian surname: Komusiewicz fullname: Komusiewicz, Christian organization: Institut für Informatik, Friedrich‐Schiller‐Universität Jena – sequence: 3 givenname: Manuel surname: Sorge fullname: Sorge, Manuel organization: Institut für Softwaretechnik und Theoretische Informatik |
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| Cites_doi | 10.1007/978-3-319-21275-3 10.1002/net.3230120103 10.1287/trsc.2013.0507 10.1137/110834810 10.1016/0377-2217(85)90252-8 10.1137/1.9781611973075.32 10.1016/j.ejor.2014.04.039 10.4230/OASIcs.ATMOS.2015.130 10.2174/1874243200802010008 10.1145/322139 10.1016/j.cor.2006.07.007 10.1007/BF01580113 10.1137/1.9781611973679.ch2 10.1137/0110015 10.1002/net.3230060306 10.1016/j.jda.2012.04.007 10.1016/j.orl.2014.05.002 10.1016/0305-0483(83)90033-6 10.1016/j.ejor.2004.01.023 10.1112/jlms/s1-10.37.26 10.1016/j.jcss.2016.06.001 10.1093/comjnl/bxm048 10.1145/367766.368168 10.1109/SFCS.1976.6 10.1016/j.cor.2009.06.018 10.1002/net.3230110308 10.1007/978-1-4471-5559-1 10.1016/0305-0548(83)90026-6 10.1137/0207017 10.1002/net.3230060305 10.1002/net.3230230304 10.1007/BFb0121091 10.1016/0305-0548(94)00070-O 10.1016/j.cor.2005.02.009 10.1016/S0305-0548(99)00031-3 10.1007/978-3-642-25870-1_28 10.1145/321105.321111 10.1137/S0895480197331454 |
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| Notes | This version describes several algorithmic enhancements, contains an experimental evaluation of our algorithm, and provides a new benchmark data set. A preliminary version of this article appeared in the Proceedings of the 15th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS’15) ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
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| Snippet | We prove that any polynomial‐time
α
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n
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‐approximation algorithm for the n‐vertex metric asymmetric Traveling Salesperson Problem yields a polynomial‐time
O... We prove that any polynomial‐time ‐approximation algorithm for the n ‐vertex metric asymmetric Traveling Salesperson Problem yields a polynomial‐time... We prove that any polynomial-time [alpha] ( n )-approximation algorithm for the n-vertex metric asymmetric Traveling Salesperson Problem yields a... |
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| SubjectTerms | Algorithms Approximation Benchmarks Chinese Postman combinatorial optimization Computer simulation fixed‐parameter algorithm Mathematical analysis NP‐hard problem Polynomials Production scheduling Rural Postman transportation vehicle routing |
| Title | A parameterized approximation algorithm for the mixed and windy capacitated arc routing problem: Theory and experiments |
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