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Probabilistic evaluation of solutions in variability-driven optimization

Published: 09 April 2006 Publication History

Abstract

VLSI design optimization requires evaluation of different solutions, to compare superiority of one over the other. Typically, a solution is superior if it has a better associated timing and cost. In the presence of fabrication variability, the timing and cost of a solution become random variables with spatial and functional correlations. Therefore the evaluation of solutions shall be performed probabilistically to determine the probability that a solution has better cost and timing. In this paper we propose and evaluate three methods for fast and accurate probabilistic comparison of solutions: 1) regular Monte Carlo simulation (as a basis of comparison), 2) joint-pdf approximation using moment matching, and 3) bound-based Conditional Monte Carlo simulation.We integrated these methods in a variability-driven leakage optimization framework using dual threshold voltages. Experimental results show that joint-pdf based approximation is very fast, however it results in sub-optimal solutions due to lower accuracy. Conditional Monte Carlo method is on average 25 times faster than regular Monte Carlo, but slower than approximating joint-pdf. It also results in additional improvement in expected leakage, when compared to joint-pdf method. Monte Carlo simulation is extremely slow and inapplicable to an optimization framework. Deterministic approaches that are based on worst-case estimates had the highest expected leakage.

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  • (2008)Statistical Timing AnalysisIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2007.90704727:4(589-607)Online publication date: 1-Apr-2008

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    cover image ACM Conferences
    ISPD '06: Proceedings of the 2006 international symposium on Physical design
    April 2006
    232 pages
    ISBN:1595932992
    DOI:10.1145/1123008
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    Published: 09 April 2006

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    • (2008)Statistical Timing AnalysisIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2007.90704727:4(589-607)Online publication date: 1-Apr-2008

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