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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.22717 |
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| _version_ | 1866929568461357056 |
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| author | Geis, Lukas Allendorf, Daniel Bläsius, Thomas Leonhardt, Alexander Meyer, Ulrich Penschuck, Manuel Tran, Hung |
| author_facet | Geis, Lukas Allendorf, Daniel Bläsius, Thomas Leonhardt, Alexander Meyer, Ulrich Penschuck, Manuel Tran, Hung |
| contents | We consider a maximum entropy edge weight model for shortest path networks 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 (i) it converges to the required distribution and (ii) that the mixing time on the cycle graph is polynomial. We then engineer an implementation of the process using a dynamic version of Johnson's algorithm in connection with a bidirectional Dijkstra search. We empirically study the performance characteristics of an implementation of the novel sampling algorithm as well as the output produced by the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22717 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform Sampling of Negative Edge Weights in Shortest Path Networks Geis, Lukas Allendorf, Daniel Bläsius, Thomas Leonhardt, Alexander Meyer, Ulrich Penschuck, Manuel Tran, Hung Data Structures and Algorithms We consider a maximum entropy edge weight model for shortest path networks 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 (i) it converges to the required distribution and (ii) that the mixing time on the cycle graph is polynomial. We then engineer an implementation of the process using a dynamic version of Johnson's algorithm in connection with a bidirectional Dijkstra search. We empirically study the performance characteristics of an implementation of the novel sampling algorithm as well as the output produced by the model. |
| title | Uniform Sampling of Negative Edge Weights in Shortest Path Networks |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2410.22717 |