We study the satisfiability 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 with $\alpha=M/N$ close to the
experimental threshold $\alpha_c$ 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 $\alpha$ is
close to (but smaller than) $\alpha_c$. We introduce a new type of message
passing algorithm which allows to find efficiently a satisfiable assignment of
the variables in the 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 are 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.

本研究介绍了一种新的消息传递算法，可有效找到困难区域内变量的满足性分配，并应用于随机生成的具有一定数量的变量、布尔运算和公式的问题中，问题的困难程度与解决思路中 “聚类” 现象相关

Survey propagation: 一种可满足性问题的算法

Survey propagation: an algorithm for satisfiability

The author presents two tricks to accelerate depth-first search algorithms
for a class of combinatorial puzzle problems, such as tiling a tray by a fixed
set of polyominoes. The first trick is to implement each assumption of the
search with reversible local operations on doubly linked lists. By this trick,
every step of the search affects the data incrementally.
The second trick is to add a ghost square that represents the identity of
each polyomino. Thus puts the rule that each polyomino be used once on the same
footing as the rule that each square be covered once. The coding simplifies to
a more abstract form which is equivalent to 0-1 integer programming. More
significantly for the total computation time, the search can naturally switch
between placing a fixed polyomino or covering a fixed square at different
stages, according to a combined heuristic.
Finally the author reports excellent performance for his algorithm for some
familiar puzzles. These include tiling a hexagon by 19 hexiamonds and the N
queens problem for N up to 18.

介绍了用于加速一类组合拼图问题的深度优先搜索算法的两个技巧，一是在双向链表上实现可逆局部操作，二是添加一个代表多米诺骨牌标识的幽灵正方形，因此算法的性能得到优化。

跳跃链接

Dancing links

An algorithm for computing the stable model semantics of logic programs is
developed. It is shown that one can extend the semantics and the algorithm to
handle new and more expressive types of rules. Emphasis is placed on the use of
efficient implementation techniques. In particular, an implementation of
lookahead that safely avoids testing every literal for failure and that makes
the use of lookahead feasible is presented. In addition, a good heuristic is
derived from the principle that the search space should be minimized.
Due to the lack of competitive algorithms and implementations for the
computation of stable models, the system is compared with three satisfiability
solvers. This shows that the heuristic can be improved by breaking ties, but
leaves open the question of how to break them. It also demonstrates that the
more expressive rules of the stable model semantics make the semantics clearly
preferable over propositional logic when a problem has a more compact logic
program representation. Conjunctive normal form representations are never more
compact than logic program ones.

提出了一种用于计算逻辑程序稳定模型语义的算法，强调使用有效的实现技术，特别地，提出了一种展望的实现和一种通过最小化搜索空间来产生良好的启发式方法。结果表明，稳定模型语义的逻辑程序具有更紧凑的逻辑程序表示，因此在某些问题上比命题逻辑优越。