Graph partitioning is a classical NP problem. The goal of graphing partition is to have as few cut edges in the graph as possible. Meanwhile, the capacity limit of the shard should be satisfied. In this paper, a model for graph partitioning is proposed. Then the model is converted into a mixed 0-1 linear programming by introducing variables. In order to solve this model, we select some variables to design the vertex relocation model. This work designs a variable selection strategy according to the effect of vertex relocation on the number of local edges. For purpose of implementing graph partitioning on large scale graph, we design an iterative algorithm to solve the model by selecting some variables in each iteration. The algorithm relocates the shard of the vertex according to the solution of the model. In the experiment, the method in this paper is simulated and compared with BLP and its related methods in the different shard sizes on the five social network datasets. The simulation results show that the method of this paper works well. In addition, we compare the effects of different parameter values and variables selection strategies on the partitioning effect.

图划分是一个经典的 NP 问题。图形划分的目标是图形中的切边尽可能少。同时，要满足分片的容量限制。本文提出了一种图划分模型。然后通过引入变量将模型转换为混合0-1线性规划。为了求解这个模型，我们选择一些变量来设计顶点重定位模型。这项工作根据顶点重定位对局部边数的影响设计了变量选择策略。为了在大规模图上实现图划分，我们设计了一种迭代算法，通过在每次迭代中选择一些变量来求解模型。该算法根据模型的解重新定位顶点的分片。在实验中，本文的方法在五个社交网络数据集上的不同分片大小下进行了模拟，并与 BLP 及其相关方法进行了比较。仿真结果表明本文方法效果良好。此外，我们还比较了不同参数值和变量选择策略对分配效果的影响。