A Multi-Level Algorithm For Partitioning Graphs

B. Hendrickson, R. Leland
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引用次数: 1300

Abstract

The graph partitioning problem is that of dividing the vertices of a graph into sets of specified sizes such that few edges cross between sets. This NP-complete problem arises in many important scientific and engineering problems. Prominent examples include the decomposition of data structures for parallel computation, the placement of circuit elements and the ordering of sparse matrix computations. We present a multilevel algorithm for graph partitioning in which the graph is approximated by a sequence of increasingly smaller graphs. The smallest graph is then partitioned using a spectral method, and this partition is propagated back through the hierarchy of graphs. A variant of the Kernighan-Lin algorithm is applied periodically to refine the partition. The entire algorithm can be implemented to execute in time proportional to the size of the original graph. Experiments indicate that, relative to other advanced methods, the multilevel algorithm produces high quality partitions at low cost.
图的多级划分算法
图划分问题是将图的顶点划分为特定大小的集合,使得集合之间很少有边交叉。这个np完全问题出现在许多重要的科学和工程问题中。突出的例子包括并行计算的数据结构分解,电路元件的放置和稀疏矩阵计算的排序。我们提出了一种多层图划分算法,其中图由一系列越来越小的图近似。然后使用谱方法对最小的图进行划分,并通过图的层次结构传播这种划分。周期性地应用Kernighan-Lin算法的一种变体来细化划分。整个算法的执行时间与原始图的大小成正比。实验表明,与其他先进方法相比,该算法能以较低的成本生成高质量的分区。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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