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Parameterized Complexity of Vehicle Routing

Authors Michelle Döring , Jan Fehse , Tobias Friedrich , Paula Marten , Niklas Mohrin , Kirill Simonov , Farehe Soheil , Jakob Timm , Shaily Verma

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Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
Keywords
  • Vehicle Routing Problem
  • Treewidth
  • Parameterized Complexity

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Abstract

The Vehicle Routing Problem (VRP) is a popular generalization of the Traveling Salesperson Problem. Instead of one salesperson traversing the entire weighted, undirected graph G, there are k vehicles available to jointly cover the set of clients C ⊆ V(G). Every vehicle must start at one of the depot vertices D ⊆ V(G) and return to its start. Capacitated Vehicle Routing (CVRP) additionally restricts the route of each vehicle by limiting the number of clients it can cover, the distance it can travel, or both.
In this work, we study the complexity of VRP and the three variants of CVRP for several parameterizations, in particular focusing on the treewidth of G. We present an FPT algorithm for VRP parameterized by treewidth. For CVRP, we prove paraNP- and W[⋅]-hardness for various parameterizations, including treewidth, thereby rendering the existence of FPT algorithms unlikely. In turn, we provide an XP algorithm for CVRP when parameterized by both treewidth and the vehicle capacity.

Cite As Get BibTex

Michelle Döring, Jan Fehse, Tobias Friedrich, Paula Marten, Niklas Mohrin, Kirill Simonov, Farehe Soheil, Jakob Timm, and Shaily Verma. Parameterized Complexity of Vehicle Routing. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.IPEC.2025.10

Author Details

Michelle Döring
  • Hasso Plattner Institute, University of Potsdam, Germany
Jan Fehse
  • Hasso Plattner Institute, University of Potsdam, Germany
Tobias Friedrich
  • Hasso Plattner Institute, University of Potsdam, Germany
Paula Marten
  • Hasso Plattner Institute, University of Potsdam, Germany
Niklas Mohrin
  • Hasso Plattner Institute, University of Potsdam, Germany
Kirill Simonov
  • Department of Informatics, University of Bergen, Norway
Farehe Soheil
  • Hasso Plattner Institute, University of Potsdam, Germany
Jakob Timm
  • Hasso Plattner Institute, University of Potsdam, Germany
Shaily Verma
  • Hasso Plattner Institute, University of Potsdam, Germany

Funding

  • Döring, Michelle: German Federal Ministry for Education and Research (BMBF) through the project "KI Servicezentrum Berlin Brandenburg" (01IS22092).

References

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