关于团簇态的局部平衡方程
On local equilibrium equations for clustering states
摘要：
本文证明了局部平衡方程（TAP方程或置信传播方程的推广）在着色问题的可着色阶段有解。同样的结果扩展到其他优化问题的解决方案成本为零（例如K-可满足性）。在一个随机图上，局部平衡方程的解与组态簇（簇态）相关联。在随机图上，局部平衡方程在无色相中几乎处处有解;在这种情况下，我们必须引入局部平衡方程的拟解的概念。
英文摘要：
In this note we show that local equilibrium equations (the generalization of the TAP equations or of the belief propagation equations) do have solutions in the colorable phase of the coloring problem. The same results extend to other optimization problems where the solutions has cost zero (e.g. K-satisfiability). On a random graph the solutions of the local equilibrium equations are associated to clusters of configurations (clustering states). On a random graph the local equilibrium equations have solutions almost everywhere in the uncolored phase; in this case we have to introduce the concept quasi-solution of the local equilibrium equations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
