This paper presents a new mathematical programming model and a solution approach for a special class of graph partitioning problem. The problem studied here is in the context of distributed web search, in which a very large world-wide-web graph is partitioned to improve the efficiency of webpage ranking (known as PageRank). Although graph partitioning problems have been widely studied and there have been several computational algorithms and mathematical programming models in the literature, the graph partitioning problem for PageRank imposes unique constraints on the density balance. This problem is called the min-cut density-balanced partitioning problem. In this paper, we propose a new mathematical programming model and a solution approach to efficiently solve this min-cut density-balanced partitioning problem. As the objective on the minimum cut and the constraint on the density balance are not the direct performance measure of PageRank, we also investigate the performance of the solutions obtained from a MIP solver and our approach on the ranking’s accuracy and the local ranking’s computation times. The experiment results show both solutions are comparable in terms of the ranking’s accuracy and the local ranking’s computation times whereas it is much faster to obtain the partitioning solutions using our approach.

中文翻译：

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最小切密度平衡分区解决方案对分布式网页排名的影响

本文提出了一种新的数学编程模型和一种针对特殊类别的图划分问题的解决方案。这里研究的问题是在分布式Web搜索的背景下进行的，其中对非常大的万维网图进行了分区以提高网页排名的效率（称为PageRank）。尽管图划分问题已经被广泛研究，并且在文献中已经有几种计算算法和数学编程模型，但PageRank的图划分问题对密度平衡施加了独特的约束。该问题称为最小切割密度平衡分配问题。在本文中，我们提出了一种新的数学编程模型和一种解决方法，可以有效解决最小切割密度平衡分区问题。由于最小割度的目标和对密度平衡的限制不是PageRank的直接性能指标，因此，我们还研究了从MIP求解器获得的解决方案的性能以及我们在排名准确性和本地排名计算时间上的方法。