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arXiv · 2011.03915

Sampling Constraint Satisfaction Solutions in the Local Lemma Regime

Weiming Feng·Kun He·Yitong Yin
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Abstract

We give a Markov chain based algorithm for sampling almost uniform solutions of constraint satisfaction problems (CSPs). Assuming a canonical setting for the Lov\'asz local lemma, where each constraint is violated by a small number of forbidden local configurations, our sampling algorithm is accurate in a local lemma regime, and the running time is a fixed polynomial whose dependency on $n$ is close to linear, where $n$ is the number of variables. Our main approach is a new technique called state compression, which generalizes the "mark/unmark" paradigm of Moitra (Moitra, JACM, 2019), and can give fast local-lemma-based sampling algorithms. As concrete applications of our technique, we give the current best almost-uniform samplers for hypergraph colorings and for CNF solutions.

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Weiming Feng, Kun He, Yitong Yin. 2020-11-08. Sampling Constraint Satisfaction Solutions in the Local Lemma Regime. https://arxiv.org/abs/2011.03915

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