A parameterized approximation algorithm for the mixed and windy capacitated arc routing problem: Theory and experiments

René van Bevern, Christian Komusiewicz, Manuel Sorge

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)262-278
Number of pages17
JournalNetworks
Volume70
Issue number3
DOIs
Publication statusPublished - 1 Oct 2017

Keywords

  • Chinese Postman
  • combinatorial optimization
  • fixed-parameter algorithm
  • NP-hard problem
  • Rural Postman
  • transportation
  • vehicle routing
  • EULERIAN EXTENSION
  • BOUNDS

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