用信念修正引导的抽取算法求解约束满足问题
Solving Constraint Satisfaction Problems through Belief Propagation-guided decimation
摘要：
消息传递算法在解决稀疏随机图上的硬约束满足问题上取得了惊人的成功。在这样的应用中，变量被顺序地固定以满足约束。消息传递在每个步骤之后运行。其结果为下一步的选择提供了启发。参照统计物理学中的类似程序，这种方法被称为“抽取”。抽取过程的行为知之甚少。在这里，我们考虑一个简单的随机抽取算法的基础上的信念传播（BP），并分析其行为的随机k-可满足性公式。特别是，我们提出了一个树模型的分析，我们猜想，它提供了渐近准确的预测在大的情况下的限制。数值模拟证实了这一猜想。
英文摘要：
Message passing algorithms have proved surprisingly successful in solving hard constraint satisfaction problems on sparse random graphs. In such applications, variables are fixed sequentially to satisfy the constraints. Message passing is run after each step. Its outcome provides an heuristic to make choices at next step. This approach has been referred to as `decimation,' with reference to analogous procedures in statistical physics. The behavior of decimation procedures is poorly understood. Here we consider a simple randomized decimation algorithm based on belief propagation (BP), and analyze its behavior on random k-satisfiability formulae. In particular, we propose a tree model for its analysis and we conjecture that it provides asymptotically exact predictions in the limit of large instances. This conjecture is confirmed by numerical simulations.
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