约束满足问题的熵景观与非Gibbs解
Entropy landscape and non-Gibbs solutions in constraint satisfaction problems
摘要：
研究随机图中双色问题解的熵景观，这是一个典型的困难约束满足问题。我们的目标是分类的解决方案的集群类型由不同的算法。在研究的第一部分中，我们使用腔方法来获得具有给定内部熵的团簇的数量，并确定问题的相图，例如动力学，刚性和SAT-UNSAT转变。在本文的第二部分中，我们分析了不同的算法，并将它们的行为定位在问题的熵景观中。例如，我们表明，基于置信传播的抽取策略的平滑版本能够找到属于次主导集群的解决方案，甚至超越了所谓的刚性过渡，其中相关的集群变得冻结。这些非平衡解属于最有可能的解冻簇。
英文摘要：
We study the entropy landscape of solutions for the bicoloring problem in random graphs, a representative difficult constraint satisfaction problem. Our goal is to classify which type of clusters of solutions are addressed by different algorithms. In the first part of the study we use the cavity method to obtain the number of clusters with a given internal entropy and determine the phase diagram of the problem, e.g. dynamical, rigidity and SAT-UNSAT transitions. In the second part of the paper we analyze different algorithms and locate their behavior in the entropy landscape of the problem. For instance we show that a smoothed version of a decimation strategy based on Belief Propagation is able to find solutions belonging to sub-dominant clusters even beyond the so called rigidity transition where the thermodynamically relevant clusters become frozen. These non-equilibrium solutions belong to the most probable unfrozen clusters.
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