Sink-free orientations: a local sampler with applications
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909492978909184 |
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| author | Anand, Konrad Freifeld, Graham Guo, Heng Wang, Chunyang Wang, Jiaheng |
| author_facet | Anand, Konrad Freifeld, Graham Guo, Heng Wang, Chunyang Wang, Jiaheng |
| contents | For sink-free orientations in graphs of minimum degree at least $3$, we show that there is a deterministic approximate counting algorithm that runs in time $O((n^{73}/\varepsilon^{72})\log(n/\varepsilon))$, a near-linear time sampling algorithm, and a randomised approximate counting algorithm that runs in time $O((n/\varepsilon)^2\log(n/\varepsilon))$, where $n$ denotes the number of vertices of the input graph and $0<\varepsilon<1$ is the desired accuracy. All three algorithms are based on a local implementation of the sink popping method (Cohn, Pemantle, and Propp, 2002) under the partial rejection sampling framework (Guo, Jerrum, and Liu, 2019). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05877 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sink-free orientations: a local sampler with applications Anand, Konrad Freifeld, Graham Guo, Heng Wang, Chunyang Wang, Jiaheng Data Structures and Algorithms Discrete Mathematics Probability For sink-free orientations in graphs of minimum degree at least $3$, we show that there is a deterministic approximate counting algorithm that runs in time $O((n^{73}/\varepsilon^{72})\log(n/\varepsilon))$, a near-linear time sampling algorithm, and a randomised approximate counting algorithm that runs in time $O((n/\varepsilon)^2\log(n/\varepsilon))$, where $n$ denotes the number of vertices of the input graph and $0<\varepsilon<1$ is the desired accuracy. All three algorithms are based on a local implementation of the sink popping method (Cohn, Pemantle, and Propp, 2002) under the partial rejection sampling framework (Guo, Jerrum, and Liu, 2019). |
| title | Sink-free orientations: a local sampler with applications |
| topic | Data Structures and Algorithms Discrete Mathematics Probability |
| url | https://arxiv.org/abs/2502.05877 |