图划分的置信传播
Belief propagation for graph partitioning
摘要：
研究了图二分问题的置信传播算法，即在固定磁化强度下铁磁伊辛模型的基态问题。应用程序的消息传递计划与一个固定的全球参数的模型是不平凡的，我们表明，磁化强度实际上可以固定在一个本地的方式内的信念传播方程。我们的方法提供了完整的相图的随机图上的二分区问题，以及一个有效的启发式求解器，我们预计是有用的分区问题的广泛应用。
英文摘要：
We study the belief propagation algorithm for the graph bi-partitioning problem, i.e. the ground state of the ferromagnetic Ising model at a fixed magnetization. Application of a message passing scheme to a model with a fixed global parameter is not banal and we show that the magnetization can in fact be fixed in a local way within the belief propagation equations. Our method provides the full phase diagram of the bi-partitioning problem on random graphs, as well as an efficient heuristic solver that we anticipate to be useful in a wide range of application of the partitioning problem.
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