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Efficient Uniform Negative Edge Weights

Authors Lukas Geis , Daniel Allendorf , Thomas Bläsius , Alexander Leonhardt , Ulrich Meyer , Manuel Penschuck , Hung Tran

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • Random Graphs
  • Shortest Path
  • Random Edge Weights
  • Negative Cycles

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Abstract

We consider a maximum entropy edge weight model that allows for negative weights. Given a graph G and possible weights W typically consisting of positive and negative values, the model selects edge weights w ∈ W^m uniformly at random from all weights that do not introduce a negative cycle. We propose an MCMC process and show that it converges to the required distribution. We then engineer an implementation of the process using a dynamic version of Johnson’s algorithm in connection with a bidirectional Dijkstra search as well as an innovative resampling method. We empirically study the performance characteristics of these novel sampling algorithms as well as the output produced by the model.

Cite As Get BibTex

Lukas Geis, Daniel Allendorf, Thomas Bläsius, Alexander Leonhardt, Ulrich Meyer, Manuel Penschuck, and Hung Tran. Efficient Uniform Negative Edge Weights. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 18:1-18:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.18

Author Details

Lukas Geis
  • Goethe University Frankfurt, Germany
Daniel Allendorf
  • Goethe University Frankfurt, Germany
Thomas Bläsius
  • Karlsruhe Institute of Technology (KIT), Germany
Alexander Leonhardt
  • Goethe University Frankfurt, Germany
Ulrich Meyer
  • Goethe University Frankfurt, Germany
Manuel Penschuck
  • University of Southern Denmark, Odense, Denmark
Hung Tran
  • Frankfurt Institute for Advanced Studies, Germany

Funding

This work was partially funded by the Deutsche Forschungsgemeinschaft (DFG) - ME 2088/5-1, ME-2088/5-2 (FOR 2975 - Algorithms, Dynamics, and Information Flow in Networks), the LOEWE program of the state Hesse (CMMS), and the Novo Nordisk Foundation grant NNF21OC0066551.

Acknowledgements

In memory of Daniel, whose sharp analytical mind and keen insights profoundly influenced this work. We thank Deepak Ajwani and Ryan O'Conner for valuable discussions on shortest path algorithms with negative weights that triggered this research, and Mia Ischebeck for her preliminary investigation of a related MCMC process.

Supplementary Materials

References

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