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YieldDriven Clock Skew Scheduling for Arbitrary Distributions of Critical Path Delays
Yanling ZHI WaiShing LUK Yi WANG Changhao YAN Xuan ZENG
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E95A
No.12
pp.21722181 Publication Date: 2012/12/01 Online ISSN: 17451337
DOI: 10.1587/transfun.E95.A.2172 Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on VLSI Design and CAD Algorithms) Category: Physical Level Design Keyword: yielddriven, clock skew scheduling, generalized Howard algorithm, generalized minimum balance algorithm,
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Summary:
Yielddriven clock skew scheduling was previously formulated as a minimum costtotime ratio cycle problem, by assuming that variational path delays are in Gaussian distributions. However in today's nanometer technology, process variations show growing impacts on this assumption, as variational delays with nonGaussian distributions have been observed on these paths. In this paper, we propose a novel yielddriven clock skew scheduling method for arbitrary distributions of critical path delays. Firstly, a general problem formulation is proposed. By integrating the cumulative distribution function (CDF) of critical path delays, the formulation is able to handle path delays with any distributions. It also generalizes the previous formulations on yielddriven clock skew scheduling and indicates their statistical interpretations. Generalized Howard algorithm is derived for finding the critical cycles of the underlying timing constraint graphs. Moreover, an effective algorithm based on minimum balancing is proposed for the overall yield improvement. Experimental results on ISCAS89 benchmarks show that, compared with two representative existing methods, our method remarkably improves the yield by 10.25% on average (up to 14.66%).

