网络源定位问题：基态能量、熵和冻结效应
The network source location problem: ground state energy, entropy and effects of freezing
摘要：
利用熵腔方法，在副本对称和一步复本对称性破缺两个层次上计算了网络源定位问题的基态熵.该制度是本研究的一个重点，是密切相关的顶点覆盖问题与随机淬火覆盖节点。由此产生的熵消息传递启发的抽取和加固算法用于确定最佳位置的源在单个实例的运输网络。并与不考虑熵效应的传统置信度传播方法进行了比较。我们发现，在玻璃相的熵信息传递启发抽取产生较低的基态能量相比，不采取熵效应的信念传播。利用极值优化算法，我们研究了基态能量和冻结中心的分数，并将算法扩展到收集熵的统计量。理论结果与极值优化结果进行了比较。
英文摘要：
Ground state entropy of the network source location problem is evaluated at both the replica symmetric level and one-step replica symmetry breaking level using the entropic cavity method. The regime that is a focus of this study, is closely related to the vertex cover problem with randomly quenched covered nodes. The resulting entropic message passing inspired decimation and reinforcement algorithms are used to identify the optimal location of sources in single instances of transportation networks. The conventional belief propagation without taking the entropic effect into account is also compared. We find that in the glassy phase the entropic message passing inspired decimation yields a lower ground state energy compared to the belief propagation without taking the entropic effect. Using the extremal optimization algorithm, we study the ground state energy and the fraction of frozen hubs, and extend the algorithm to collect statistics of the entropy. The theoretical results are compared with the extremal optimization results.
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