Highly efficient gradient computation for density-constrained analytical placement methods

  • Authors:
  • Jason Cong;Guojie Luo

  • Affiliations:
  • University of California: Los Angeles, Los Angeles, CA, USA;University of California: Los Angeles, Los Angeles, CA, USA

  • Venue:
  • Proceedings of the 2008 international symposium on Physical design
  • Year:
  • 2008

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Abstract

Recent analytical global placers use density constraints to approximate non-overlap constraints and show very successful results. In this paper we unify a wide range of density smoothing techniques that we call global smoothing, and present a highly efficient method to compute the gradient of such smoothed densities used in several well-known analytical placers [3, 5, 7]. Our method reduces the complexity of the gradient computation by a factor of n compared to a naïve method, where n is the number of modules. Furthermore, with this efficient gradient computation we can come up with an efficient nonlinear programming-based placement framework, which supercedes the existing force-directed placement methods [4, 7]. An application of our technique, as the engine of a multilevel placer, achieved 13% and 15% wirelength improvement compared with SCAMPI [13] and mPL6 [3] on IBM-HB+ benchmark [13]