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基于再聚类和离散优化的k路划分算法

k-Way Partitioning Algorithm Based on Re-Clustering and Discrete Optimization

  • 摘要: 为了寻得集成电路更优的k路划分,提出将再聚类和离散优化应用于k路划分算法.首先利用再聚类缩小超图规模,即根据给定划分计算顶点间的评级函数值,依据取值大小进行顶点聚类;然后将超图转换为星型图,并将k路划分问题转换为无约束的离散优化问题;进而设计一个算法迭代移动增益值最大的顶点,在算法求解过程中放宽平衡约束,允许暂时处于不可行域的解,扩大问题的求解空间.在同一平台上使用ISPD98电路测试基准对所提算法、hMETIS-Kway和KaHyPar-K进行测试,并比较最小割值和运行时间.实验结果表明该算法优于hMETIS-Kway,特别是在k=2时,最小割值减少了0.173,速度提升了0.706.此外,该算法对KaHyPar-K也有相应的改进效果.

     

    Abstract: To achieve a better partitioning of VLSI circuit, re-clustering and discrete optimization are applied to the k-way partitioning algorithm. Firstly, re-clustering is used to reduce the scale of hypergraph, i.e., the rating function value between two vertices is calculated according to the given partitionings, and vertices are clustered according to the magnitude of the rating function values. Secondly, the hypergraph is converted to a star graph, and the k-way partitioning problem is transformed to an unconstrained discrete optimization problem. In turn, an algorithm is designed to iteratively move the vertices with the largest gain. During the solution process, the balancing constraints are relaxed, allowing a solution to be temporarily in the infeasible region, which expands the solution space of the problem. The proposed algorithm, hMETIS-Kway and KaHyPar-K are tested on the same platform on the ISPD98 test benchmarks, and the min-cut and running time are compared. Experimental results show that, the proposed algorithm is superior to hMETIS-Kway, especially when k=2, for which the min-cut is reduced by 0.173 and the runtime is sped up by 0.706. The proposed algorithm has almost the same improvement effect over KaHyPar-K.

     

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