警示传播算法收敛的充分条件

信息传播算法求解可满足问题时有惊人的效果，难解区域变窄.然而，因子图带有环的实例，信息传播算法不总有效，常表现为不收敛.对于这种现象，至今缺少系统的理论解释.警示传播（warning propagation，简称WP）算法是一种基础的信息传播算法，对WP算法的收敛性研究是其他信息传播算法收敛性研究的重要基础.在WP算法中，将警示信息的取值从{0，1}松弛为0，1]，利用压缩函数的性质，给出了WP算法收敛的一个充分条件.选取了两组不同规模的随机3-SAT实例进行实验模拟，结果表明：当子句与变元的比值α<1.8时，该判定条件有效.

Sufficient Conditions for Convergence of the Warning Propagation Algorithm

Message propagation algorithms are very effective in finding satisfying assignments for SAT instances, and hard region become narrower. However, message propagation algorithms do not always converge for graphs with cycles. Unfortunately, rigorous theory proof of this phenomenon is still lacking. Warning propagation (WP) algorithm is the most basic message propagation algorithm, we have derived the sufficient conditions for convergence of the warning propagation algorithm. Lastly, experimental results show that such conditions for convergence of WP are very effective in different group data from random satisfiable 3-SAT instances.