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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2102.00970 |
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| _version_ | 1866911123195822080 |
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| author | Coja-Oghlan, Amin Cooley, Oliver Kang, Mihyun Lee, Joon Ravelomanana, Jean B. |
| author_facet | Coja-Oghlan, Amin Cooley, Oliver Kang, Mihyun Lee, Joon Ravelomanana, Jean B. |
| contents | Warning Propagation is a combinatorial message passing algorithm that unifies and generalises a wide variety of recursive combinatorial procedures. Special cases include the Unit Clause Propagation and Pure Literal algorithms for satisfiability as well as the peeling process for identifying the $k$-core of a random graph. Here we analyse Warning Propagation in full generality on the binomial random graph. We prove that under a mild stability assumption Warning Propagation converges rapidly. In effect, the analysis of the fixed point of the message passing process on a random graph reduces to analysing the process on a Galton-Watson tree. This result corroborates and generalises a heuristic first put forward by Pittel, Spencer and Wormald in their seminal $k$-core paper (JCTB 1996). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_00970 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Warning Propagation on random graphs Coja-Oghlan, Amin Cooley, Oliver Kang, Mihyun Lee, Joon Ravelomanana, Jean B. Combinatorics 05C80 Warning Propagation is a combinatorial message passing algorithm that unifies and generalises a wide variety of recursive combinatorial procedures. Special cases include the Unit Clause Propagation and Pure Literal algorithms for satisfiability as well as the peeling process for identifying the $k$-core of a random graph. Here we analyse Warning Propagation in full generality on the binomial random graph. We prove that under a mild stability assumption Warning Propagation converges rapidly. In effect, the analysis of the fixed point of the message passing process on a random graph reduces to analysing the process on a Galton-Watson tree. This result corroborates and generalises a heuristic first put forward by Pittel, Spencer and Wormald in their seminal $k$-core paper (JCTB 1996). |
| title | Warning Propagation on random graphs |
| topic | Combinatorics 05C80 |
| url | https://arxiv.org/abs/2102.00970 |