Exact and approximation algorithms for routing a convoy through a graph

Martijn van Ee*, Tim Oosterwijk, René Sitters, Andreas Wiese

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

We study routing problems of a convoy in a graph, generalizing the shortest path problem (SPP), the travelling salesperson problem (TSP), and the Chinese postman problem (CPP) which are all well-studied in the classical (non-convoy) setting. We assume that each edge in the graph has a length and a speed at which it can be traversed and that our convoy has a given length. While the convoy moves through the graph, parts of it can be located on different edges. For safety requirements, at all time the whole convoy needs to travel at the same speed which is dictated by the slowest edge on which currently a part of the convoy is located. For Convoy-SPP, we give a strongly polynomial time exact algorithm. For Convoy-TSP, we provide an O(logn)-approximation algorithm and an O(1)-approximation algorithm for trees. Both results carry over to Convoy-CPP which—maybe surprisingly—we prove to be NP-hard in the convoy setting. This contrasts the non-convoy setting in which the problem is polynomial time solvable.

Original languageEnglish
Number of pages24
JournalMathematical Programming
DOIs
Publication statusAccepted/In press - 2025

Bibliographical note

Publisher Copyright:
© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2024.

Keywords

  • 68Q25
  • 68W25
  • 90C27
  • 90C39
  • Approximation algorithms
  • Convoy routing
  • Shortest path problem
  • Traveling salesperson problem

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