Uniform Sampling through the Lov\'asz Local Lemma
Data Structures and Algorithms
2019-01-16 v4 Combinatorics
Probability
Abstract
We propose a new algorithmic framework, called "partial rejection sampling", to draw samples exactly from a product distribution, conditioned on none of a number of bad events occurring. Our framework builds (perhaps surprising) new connections between the variable framework of the Lov\'asz Local Lemma and some classical sampling algorithms such as the "cycle-popping" algorithm for rooted spanning trees. Among other applications, we discover new algorithms to sample satisfying assignments of k-CNF formulas with bounded variable occurrences.
Cite
@article{arxiv.1611.01647,
title = {Uniform Sampling through the Lov\'asz Local Lemma},
author = {Heng Guo and Mark Jerrum and Jingcheng Liu},
journal= {arXiv preprint arXiv:1611.01647},
year = {2019}
}
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29 pages