Uniform Sampling Through the Lovász Local Lemma
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TLDR
This framework builds new connections between the variable framework of the Lovász Local Lemma and some classical sampling algorithms such as the cycle-popping algorithm for rooted spanning trees and new algorithms to sample satisfying assignments of k-CNF formulas with bounded variable occurrences.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 new connections between the variable framework of the Lovasz 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.read more
Citations
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Journal ArticleDOI
New bounds for the Moser‐Tardos distribution
TL;DR: In this article, the MT-distribution is shown to satisfy an approximate independence condition asymptotically stronger than the Lovasz Local Lemma (LLL) distribution.
Proceedings ArticleDOI
Fast sampling and counting -SAT solutions in the local lemma regime
TL;DR: The main technical contribution is to use the local lemma to bypass the connectivity barrier in traditional Markov chain approaches, which makes the well developed MCMC method applicable on disconnected state spaces such as SAT solutions.
Posted Content
Towards the sampling Lovász Local Lemma.
TL;DR: For the special case of properly coloring $k, q=O(1)$ and uniform hypergraphs, the term $Delta^{7}$ improves the previously best known $\Delta^{14}$ for deterministic algorithms and $ Delta^{13} for randomized algorithms.
Posted Content
Sampling Constraint Satisfaction Solutions in the Local Lemma Regime
Weiming Feng,Kun He,Yitong Yin +2 more
TL;DR: A Markov chain based algorithm for sampling almost uniform solutions of constraint satisfaction problems (CSPs) that generalizes the “mark/unmark” paradigm of Moitra, and can give fast local-lemma-based sampling algorithms.
Posted Content
Perfect sampling from spatial mixing.
Weiming Feng,Heng Guo,Yitong Yin +2 more
TL;DR: It is shown that strong spatial mixing with a rate faster than the growth of neighborhood implies the existence of efficient perfect samplers for spin systems, and the currently best perfect sampling algorithms for colorings in bounded degree graphs and in graphs with sub-exponential neighborhood growth are given.
References
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Exact sampling with coupled Markov chains and applications to statistical mechanics
James Propp,David B. Wilson +1 more
TL;DR: In this paper, a variant of the ergodic aperiodic Markov chain sampling method is proposed, which runs from a distant point in the past up to the present, where the distance into the past that one needs to go is determined during the running of the algorithm itself.
Proceedings ArticleDOI
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Journal ArticleDOI
A constructive proof of the general lovász local lemma
Robin A. Moser,Gábor Tardos +1 more
TL;DR: The Lovasz Local Lemma algorithm as mentioned in this paper is a powerful tool to nonconstructively prove the existence of combinatorial objects meeting a prescribed collection of criteria, and it has been used in many applications.
Proceedings ArticleDOI
Counting independent sets up to the tree threshold
TL;DR: It is shown that on any graph of maximum degree Δ correlations decay with distance at least as fast as they do on the regular tree of the same degree, which resolves an open conjecture in statistical physics.
Book
The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability
TL;DR: The SAT solvers can now routinely find solutions to practical problems that involve millions of variables and were thought until very recently to be hopelessly difficult as discussed by the authors, and they have led to game-changing applications in industry.