采样 Lovász 局部引理
A sampling Lovász Local Lemma
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中文总结 AI 辅助
本文提出一种采样 Lovász 局部引理算法，在满足特定条件时，利用近似计数子程序，在多项式时间内生成总变差距离内均匀的满足赋值。
中文摘要 AI 辅助
我们给出了一个近似均匀采样器，用于满足约束满足问题的满足赋值，该问题满足 $4\mathrm e p(\Delta+1)^2\le1$，其中 $p$ 是均匀乘积分布下最大的约束违反概率，$\Delta$ 是依赖图的最大度。该算法调用 Liu、Wang、Yin、Zhang 和 Zhou 最近的高效近似计数算法作为子程序，并在 $(n+m/\varepsilon)^{O(k\Delta\log D)}$ 时间内返回一个在总变差距离 $\varepsilon$ 内均匀分布的满足赋值，其中 $n$ 和 $m$ 分别是变量和约束的数量，$D$ 是公共定义域大小，$k$ 约束了约束的元数。
英文摘要
We give an approximately uniform sampler for satisfying assignments of constraint satisfaction problems that satisfy $4\mathrm e p(Δ+1)^2\le1$, where $p$ is the largest constraint-violation probability under the uniform product distribution, and $Δ$ is the maximum degree of the dependency graph. The algorithm invokes the recent efficient approximate counting algorithm of Liu, Wang, Yin, Zhang, and Zhou~\cite{CountingLLL} as a subroutine and returns a satisfying assignment sampled within total-variation distance $\varepsilon$ of the uniform distribution in $(n+m/\varepsilon)^{O(kΔ\log D)}$ time, where $n$ and $m$ are the numbers of variables and constraints, $D$ is the common domain size, and $k$ bounds the constraint arity. We also give an asymmetric product-form condition under which both counting and sampling are efficient. To supply the counts needed in the additional regime, we extend the marginal-expansion proof of Liu et al.
发表机构
- University of Athens（雅典大学）
机构由 AI 辅助整理，请以论文原文为准。
