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DOI: 10.4230/LIPIcs.ESA.2026.18

Efficient Uniform Negative Edge Weights

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

Published in: LIPIcs, Volume 388, 34th Annual European Symposium on Algorithms (ESA 2026)

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.

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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)

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@InProceedings{geis_et_al:LIPIcs.ESA.2026.18,
  author =	{Geis, Lukas and Allendorf, Daniel and Bl\"{a}sius, Thomas and Leonhardt, Alexander and Meyer, Ulrich and Penschuck, Manuel and Tran, Hung},
  title =	{{Efficient Uniform Negative Edge Weights}},
  booktitle =	{34th Annual European Symposium on Algorithms (ESA 2026)},
  pages =	{18:1--18:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-445-1},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{388},
  editor =	{Bille, Philip and Pettie, Seth and Storandt, Sabine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2026.18},
  URN =		{urn:nbn:de:0030-drops-271542},
  doi =		{10.4230/LIPIcs.ESA.2026.18},
  annote =	{Keywords: Random Graphs, Shortest Path, Random Edge Weights, Negative Cycles}
}

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Efficient Uniform Negative Edge Weights

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