Non-Pool-Based Line Planning on Graphs of Bounded Treewidth

Authors Irene Heinrich , Philine Schiewe , Constantin Seebach

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Author Details

Irene Heinrich
  • TU Darmstadt, Germany
Philine Schiewe
  • Aalto University, Espoo, Finland
Constantin Seebach
  • RPTU Kaiserslautern-Landau, Kaiserslautern, Germany


This work was partially developed during a guest stay of the first author at the Aalto University in Espoo, Finland.

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Irene Heinrich, Philine Schiewe, and Constantin Seebach. Non-Pool-Based Line Planning on Graphs of Bounded Treewidth. In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Line planning, i.e. choosing routes which are to be serviced by vehicles in order to satisfy network demands, is an important aspect of public transport planning. While there exist heuristic procedures for generating lines from scratch, most theoretical investigations consider the problem of choosing lines only from a predefined line pool. We consider the line planning problem when all simple paths can be used as lines and present an algorithm which is fixed-parameter tractable, i.e. it is efficient on instances with small parameter. As a parameter we consider the treewidth of the public transport network, along with its maximum degree as well as the maximum allowed frequency.

Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • Theory of computation → Fixed parameter tractability
  • Mathematics of computing → Integer programming
  • Theory of computation → Discrete optimization
  • line planning
  • public transport
  • treewidth
  • integer programming
  • fixed parameter tractability


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