Document Open Access Logo

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

Authors Irene Heinrich , Philine Schiewe , Constantin Seebach



PDF
Thumbnail PDF

File

OASIcs.ATMOS.2023.4.pdf
  • Filesize: 0.69 MB
  • 19 pages

Document Identifiers

Author Details

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

Acknowledgements

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

Cite AsGet BibTex

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)
https://doi.org/10.4230/OASIcs.ATMOS.2023.4

Abstract

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
Keywords
  • line planning
  • public transport
  • treewidth
  • integer programming
  • fixed parameter tractability

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Stefan Arnborg and Andrzej Proskurowski. Linear time algorithms for np-hard problems restricted to partial k-trees. Discret. Appl. Math., 23(1):11-24, 1989. URL: https://doi.org/10.1016/0166-218X(89)90031-0.
  2. Hans L. Bodlaender. A tourist guide through treewidth. Acta Cybern., 11(1-2):1-21, 1993. URL: https://cyber.bibl.u-szeged.hu/index.php/actcybern/article/view/3417.
  3. Hans L. Bodlaender. A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput., 25(6):1305-1317, 1996. URL: https://doi.org/10.1137/S0097539793251219.
  4. Hans L. Bodlaender. A partial k-arboretum of graphs with bounded treewidth. Theor. Comput. Sci., 209(1-2):1-45, 1998. URL: https://doi.org/10.1016/S0304-3975(97)00228-4.
  5. Ralf Borndörfer, Martin Grötschel, and Marc E. Pfetsch. A column-generation approach to line planning in public transport. Transp. Sci., 41(1):123-132, 2007. URL: https://doi.org/10.1287/trsc.1060.0161.
  6. Simon Bull, Jesper Larsen, Richard Martin Lusby, and Natalia J. Rezanova. Optimising the travel time of a line plan. 4OR, 17(3):225-259, 2019. URL: https://doi.org/10.1007/s10288-018-0391-5.
  7. Michael R. Bussieck, Peter Kreuzer, and Uwe T. Zimmermann. Optimal lines for railway systems. European Journal of Operational Research, 96(1):54-63, 1997. URL: https://doi.org/10.1016/0377-2217(95)00367-3.
  8. M. T. Claessens, Nico M. van Dijk, and Peter J. Zwaneveld. Cost optimal allocation of rail passenger lines. Eur. J. Oper. Res., 110(3):474-489, 1998. URL: https://doi.org/10.1016/S0377-2217(97)00271-3.
  9. Bruno Courcelle. The monadic second-order logic of graphs. i. recognizable sets of finite graphs. Inf. Comput., 85(1):12-75, 1990. URL: https://doi.org/10.1016/0890-5401(90)90043-H.
  10. Robert Ganian, Sebastian Ordyniak, and M. S. Ramanujan. Going beyond primal treewidth for (M)ILP. In Satinder Singh and Shaul Markovitch, editors, Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, February 4-9, 2017, San Francisco, California, USA, pages 815-821. AAAI Press, 2017. URL: http://aaai.org/ocs/index.php/AAAI/AAAI17/paper/view/14272.
  11. Philine Gattermann, Jonas Harbering, and Anita Schöbel. Line pool generation. Public Transp., 9(1-2):7-32, 2017. URL: https://doi.org/10.1007/s12469-016-0127-x.
  12. Marc Goerigk and Marie Schmidt. Line planning with user-optimal route choice. Eur. J. Oper. Res., 259(2):424-436, 2017. URL: https://doi.org/10.1016/j.ejor.2016.10.034.
  13. Valérie Guihaire and Jin-Kao Hao. Transit network design and scheduling: A global review. Transportation Research Part A: Policy and Practice, 42(10):1251-1273, 2008. URL: https://doi.org/10.1016/j.tra.2008.03.011.
  14. Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual, 2023. URL: https://www.gurobi.com.
  15. Irene Heinrich, Philine Schiewe, and Constantin Seebach. Algorithms and hardness for non-pool-based line planning. In Mattia D'Emidio and Niels Lindner, editors, 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, ATMOS 2022, September 8-9, 2022, Potsdam, Germany, volume 106 of OASIcs, pages 8:1-8:21. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/OASIcs.ATMOS.2022.8.
  16. Ton Kloks. Treewidth: computations and approximations, volume 842 of Lecture Notes in Computer Science. Springer-Verlag Berlin Heidelberg, 1994. URL: https://doi.org/10.1007/BFb0045375.
  17. Berenike Masing, Niels Lindner, and Ralf Borndörfer. The price of symmetric line plans in the parametric city, 2022. URL: https://arxiv.org/abs/2201.09756.
  18. Neil Robertson and Paul D. Seymour. Graph minors. II. algorithmic aspects of tree-width. J. Algorithms, 7(3):309-322, 1986. URL: https://doi.org/10.1016/0196-6774(86)90023-4.
  19. Alexander Schiewe, Philine Schiewe, and Marie Schmidt. The line planning routing game. Eur. J. Oper. Res., 274(2):560-573, 2019. URL: https://doi.org/10.1016/j.ejor.2018.10.023.
  20. Anita Schöbel. Line planning in public transportation: models and methods. OR Spectr., 34(3):491-510, 2012. URL: https://doi.org/10.1007/s00291-011-0251-6.
  21. Anita Schöbel and Susanne Scholl. Line planning with minimal traveling time. In Leo G. Kroon and Rolf H. Möhring, editors, 5th Workshop on Algorithmic Methods and Models for Optimization of Railways, ATMOS 2005, September 14, 2005, Palma de Mallorca, Spain, volume 2 of OASIcs. Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, Germany, 2005. URL: http://drops.dagstuhl.de/opus/volltexte/2006/660.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail