ePlace: Electrostatics-Based Placement Using Fast Fourier Transform and Nesterov's Method

We develop a flat, analytic, and nonlinear placement algorithm, ePlace, which is more effective, generalized, simpler, and faster than previous works. Based on the analogy between placement instance and electrostatic system, we develop a novel placement density function eDensity, which models every object as positive charge and the density cost as the potential energy of the electrostatic system. The electric potential and field distribution are coupled with density using a well-defined Poisson's equation, which is numerically solved by spectral methods based on fast Fourier transform (FFT). Instead of using the conjugate gradient (CG) nonlinear solver in previous placers, we propose to use Nesterov's method which achieves faster convergence. The efficiency bottleneck on line search is resolved by predicting the steplength using a closed-form equation of Lipschitz constant. The placement performance is validated through experiments on the ISPD 2005 and ISPD 2006 benchmark suites, where ePlace outperforms all state-of-the-art placers (Capo10.5, FastPlace3.0, RQL, MAPLE, ComPLx, BonnPlace, POLAR, APlace3, NTUPlace3, mPL6) with much shorter wirelength and shorter or comparable runtime. On average, of all the ISPD 2005 benchmarks, ePlace outperforms the leading placer BonnPlace with 2.83% shorter wirelength and runs 3.05× faster; and on average, of all the ISPD 2006 benchmarks, ePlace outperforms the leading placer MAPLE with 4.59% shorter wirelength and runs 2.84× faster.