Borel version of the Local Lemma
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2016
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| Subjects: | |
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| _version_ | 1866913250725068800 |
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| author | Csóka, Endre Grabowski, Łukasz Máthé, András Pikhurko, Oleg Tyros, Konstantinos |
| author_facet | Csóka, Endre Grabowski, Łukasz Máthé, András Pikhurko, Oleg Tyros, Konstantinos |
| contents | We prove a Borel version of the local lemma, i.e. we show that, under suitable assumptions, if the set of variables in the local lemma has a structure of a Borel space, then there exists a satisfying assignment which is a Borel function. The main tool which we develop for the proof, which is of independent interest, is a parallel version of the Moser-Tardos algorithm which uses the same random bits to resample clauses that are far enough in the dependency graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1605_04877 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Borel version of the Local Lemma Csóka, Endre Grabowski, Łukasz Máthé, András Pikhurko, Oleg Tyros, Konstantinos Combinatorics Dynamical Systems Probability We prove a Borel version of the local lemma, i.e. we show that, under suitable assumptions, if the set of variables in the local lemma has a structure of a Borel space, then there exists a satisfying assignment which is a Borel function. The main tool which we develop for the proof, which is of independent interest, is a parallel version of the Moser-Tardos algorithm which uses the same random bits to resample clauses that are far enough in the dependency graph. |
| title | Borel version of the Local Lemma |
| topic | Combinatorics Dynamical Systems Probability |
| url | https://arxiv.org/abs/1605.04877 |