一种快速增量周期比算法

Gang Wu, C. Chu
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引用次数: 0

摘要

本文提出了一种在增量变化的有向循环图上快速求出最大循环比的算法。与传统的MCR算法在每次增量变化时都需要重新计算所有内容相比,我们的算法只需利用变化前的MCR和相应的最大周期即可有效地找到MCR。特别是,前面的MCR允许我们在更改节点处安全地破坏图。然后,我们通过求解无正循环图上的单源最长路径问题来检测MCR的变化方向。提出了一种距离桶法来加快寻找最长路径的过程。我们的算法根据检测到的MCR是增加还是减少继续向上或向下搜索。通过改进的Karp-Orlin算法重用循环检测中发现的最长路径,快速向下搜索。此外,本文还提出了一种成本转移的思想,以避免在特定类型的增量变化上计算MCR。我们在随机图和电路基准上评估了我们的算法。提出了一种应用该算法的定时驱动的详细布局方法。与Howard和Karp-Orlin MCR算法相比,我们的算法在随机图和电路测试中都显示出更高的MCR查找效率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Fast Incremental Cycle Ratio Algorithm
In this paper, we propose an algorithm to quickly find the maximum cycle ratio (MCR) on an incrementally changing directed cyclic graph. Compared with traditional MCR algorithms which have to recalculate everything from scratch at each incremental change, our algorithm efficiently finds the MCR by just leveraging the previous MCR and the corresponding largest cycle before the change. In particular, the previous MCR allows us to safely break the graph at the changed node. Then, we can detect the changing direction of the MCR by solving a single source longest path problem on a graph without positive cycle. A distance bucket approach is proposed to speed up the process of finding the longest paths. Our algorithm continues to search upward or downward based on whether the MCR is detected as increased or decreased. The downward search is quickly performed by a modified Karp-Orlin algorithm reusing the longest paths found during the cycle detection. In addition, a cost shifting idea is proposed to avoid calculating MCR on certain type of incremental changes. We evaluated our algorithm on both random graphs and circuit benchmarks. A timing-driven detailed placement approach which applies our algorithm is also proposed. Compared with Howard's and Karp-Orlin MCR algorithm, our algorithm shows much more efficiency on finding the MCR in both random graphs and circuit benchmarks.
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