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arXiv · 2410.22717

Efficient Uniform Negative Edge Weights

Lukas Geis·Daniel Allendorf·Thomas Bläsius·Alexander Leonhardt·Ulrich Meyer·Manuel Penschuck·Hung Tran
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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 $\mathcal{W}$ typically consisting of positive and negative values, the model selects edge weights $w \in \mathcal{W}^m$ 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, Hung Tran. 2024-10-30. Efficient Uniform Negative Edge Weights. https://arxiv.org/abs/2410.22717

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