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.
From: Lukas Geis [view email]
[v1]
Wed, 30 Oct 2024 05:57:37 UTC (2,082 KB)
[v2]
Tue, 21 Jul 2026 12:00:08 UTC (3,159 KB)
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