Abstract: During the coarsening phase of multilevel method，this paper introduces the concept of core and proposes the Core-Sorted Heavy-Edge Matching（CSHEM） algorithm in accordance with the compressed storage format of graph.The CSHEM algorithm not only improves previous matching schemes which are based on local information of vertex，using the global information of the finest graph core to develop its guidance role，but overcomes the defect that can only choose the Random Matching（RM） algorithm as a guide matching algorithm.Furthermore，it also presents an effective matching-based coarsening scheme that uses the CSHEM algorithm on the finest graph and the Sorted Heavy-Edge Matching（SHEM） algorithm on the coarser graphs.The scheme plays a guidance role of the core so as to make the coarser graph in accordance with the core-consistent principle.The experiment and the analysis based on ISPD98 circuit benchmark show the scheme produces encouraging performance improvement compared with those produced by the combination scheme of RM and SHEM of MeTiS that is a state-of-the-art partitioner in the literature.

Key words: core, matching algorithm, compressed storage format, undirected graph

摘要： 将图核概念引入到多水平方法粗化阶段，针对图的压缩存储格式提出了核排序重边匹配（CSHEM）算法。该算法借助图核的全局信息，改进了以往仅仅利用结点的度等局部信息进行匹配的粗化算法，在对原始图粗化过程中发挥结点核值导向性作用，克服以往只能选择随机匹配（RM）算法作为导向匹配算法的缺陷；提出了基于CSHEM和重边匹配（HEM）算法的组合粗化策略，在发挥结点核值的导向性作用的同时，又不至于被过分强调而使粗化图违背结点核值大小均匀分布的原则。基于ISPD98电路测试基准的实验和分析表明，相比无向图剖分软件MeTiS采用的RM和HEM算法的组合粗化策略，提出的策略取得了一定性能的改进。

关键词: 图核, 匹配算法, 压缩存储格式, 无向图