Survey propagation:: An algorithm for satisfiability
Survey propagation:: An algorithm for satisfiability
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DOI：
10.1002/rsa.20057
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发表时间：
2005-09-01
影响因子：
1
通讯作者：
Zecchina, R
中科院分区：
文献类型：
--
作者：
Braunstein, A;Mézard, M;Zecchina, R
本文研究了N个布尔变量上由恰好K个文字的M个子句构成的随机生成公式的可满足性。对于给定的N值，已知当alpha = M/N接近实验阈值ce时问题最困难，将几乎所有公式都SAT的区域与所有公式都UNSAT的区域分开。最近的统计物理分析的结果表明，困难是有关的解决方案的聚类现象的存在时，接近（但小于）CE，我们引入了一种新类型的消息传递算法，它允许有效地找到一个满意的分配变量在这个困难的区域。该算法是迭代的，由两个主要部分组成。第一个是消息传递过程，它概括了通常的方法，如和积或信念传播：它传递的消息可以被认为是对普通消息集群的调查。第二部分使用从调查中获得的详细概率信息，以确定变量并简化问题。最终，剩下的简化问题通过传统的启发式算法得到解决。(c)2005 Wiley Periodicals，Inc.
We study the satistiability of randomly generated formulas formed by M clauses of exactly K literals over N Boolean variables. For a given value of N the problem is known to be most difficult when alpha = M/N is close to the experimental threshold ce, separating the region where almost all formulas are SAT from the region where all formulas are UNSAT. Recent results from a statistical physics analysis suggest that the difficulty is related to the existence of a clustering phenomenon of the solutions when a is close to (but smaller than) ce, We introduce a new type of message passing algorithm which allows to find efficiently a satisfying assignment of the variables in this difficult region. This algorithm is iterative and composed of two main parts. The first is a message-passing procedure which generalizes the usual methods like Sum-Product or Belief Propagation: It passes messages that may be thought of as surveys over clusters of the ordinary messages. The second part uses the detailed probabilistic information obtained from the surveys in order to fix variables and simplify the problem. Eventually, the simplified problem that remains is solved by a conventional heuristic. (c) 2005 Wiley Periodicals, Inc.