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GOALPlace: Begin with the End in Mind

Anthony Agnesina, Rongjian Liang, Geraldo Pradipta, Anand Rajaram, Haoxing Ren

TL;DR

GOALPlace tackles placement congestion by learning from post-route cell densities and using an empirical Bayes framework to adapt density targets to a specific placer, enabling end-to-end optimization without explicit congestion estimation. The method combines hierarchical netlist clustering analysis, a James–Stein estimator for density targets, and cell-inflation-based enforcement integrated into DREAMPlace and AutoDMP. Key contributions include a statistically grounded density target derivation, timing-aware enhancements, and demonstrated QoR improvements across industrial and academic benchmarks, including up to 10x fewer DRC violations and notable reductions in wirelength and WNS/TNS. The approach is data-efficient, tool-agnostic, and scalable to large designs, offering practical impact for modern heavy-density IC flows and design space exploration.

Abstract

Co-optimizing placement with congestion is integral to achieving high-quality designs. This paper presents GOALPlace, a new learning-based general approach to improving placement congestion by controlling cell density. Our method efficiently learns from an EDA tool's post-route optimized results and uses an empirical Bayes technique to adapt this goal/target to a specific placer's solutions, effectively beginning with the end in mind. It enhances correlation with the long-running heuristics of the tool's router and timing-opt engine -- while solving placement globally without expensive incremental congestion estimation and mitigation methods. A statistical analysis with a new hierarchical netlist clustering establishes the importance of density and the potential for an adequate cell density target across placements. Our experiments show that our method, integrated as a demonstration inside an academic GPU-accelerated global placer, consistently produces macro and standard cell placements of superior or comparable quality to commercial tools. Our empirical Bayes methodology also allows a substantial quality improvement over state-of-the-art academic mixed-size placers, achieving up to 10x fewer design rule check (DRC) violations, a 5% decrease in wirelength, and a 30% and 60% reduction in worst and total negative slack (WNS/TNS).

GOALPlace: Begin with the End in Mind

TL;DR

GOALPlace tackles placement congestion by learning from post-route cell densities and using an empirical Bayes framework to adapt density targets to a specific placer, enabling end-to-end optimization without explicit congestion estimation. The method combines hierarchical netlist clustering analysis, a James–Stein estimator for density targets, and cell-inflation-based enforcement integrated into DREAMPlace and AutoDMP. Key contributions include a statistically grounded density target derivation, timing-aware enhancements, and demonstrated QoR improvements across industrial and academic benchmarks, including up to 10x fewer DRC violations and notable reductions in wirelength and WNS/TNS. The approach is data-efficient, tool-agnostic, and scalable to large designs, offering practical impact for modern heavy-density IC flows and design space exploration.

Abstract

Co-optimizing placement with congestion is integral to achieving high-quality designs. This paper presents GOALPlace, a new learning-based general approach to improving placement congestion by controlling cell density. Our method efficiently learns from an EDA tool's post-route optimized results and uses an empirical Bayes technique to adapt this goal/target to a specific placer's solutions, effectively beginning with the end in mind. It enhances correlation with the long-running heuristics of the tool's router and timing-opt engine -- while solving placement globally without expensive incremental congestion estimation and mitigation methods. A statistical analysis with a new hierarchical netlist clustering establishes the importance of density and the potential for an adequate cell density target across placements. Our experiments show that our method, integrated as a demonstration inside an academic GPU-accelerated global placer, consistently produces macro and standard cell placements of superior or comparable quality to commercial tools. Our empirical Bayes methodology also allows a substantial quality improvement over state-of-the-art academic mixed-size placers, achieving up to 10x fewer design rule check (DRC) violations, a 5% decrease in wirelength, and a 30% and 60% reduction in worst and total negative slack (WNS/TNS).
Paper Structure (30 sections, 1 theorem, 24 equations, 7 figures, 5 tables, 1 algorithm)

This paper contains 30 sections, 1 theorem, 24 equations, 7 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and Motivations
  3. Related Work
  4. Congestion Estimation and Mitigation
  5. Newer Learning-Based Approaches
  6. Density Analysis with Clustering
  7. Clustering Method
  8. Density Analysis
  9. Methodology
  10. Target Density Selection
  11. Target Density Computation
  12. Target Density Adaptation with Empirical Bayes
  13. Placer Density Distribution
  14. Mathematical Framework
  15. James--Stein Estimator
  16. ...and 15 more sections

Key Result

theorem 1

For $N\geq3$, the James--Stein estimator everywhere dominates the MLE in terms of expected total squared error (the "risk" $R$); that is, for every choice of $\textrm{$\boldsymbol{\mu}$}$.

Figures (7)

  • Figure 1: The traditional incremental routability-driven method vs. GOALPlace, our placement congestion mitigation approach based on cell density and empirical Bayes. Key steps include: (a) Generate a learning goal from a post-route optimized netlist; (b) Use the specific placer to generate cell densities based on the goal from Step (a); (c) Apply the empirical Bayes approach to refine the goal for the placer; (d) Utilize this refined goal to produce high-quality placements. This methodology is versatile and applicable to any tool flow and placer.
  • Figure 2: Visual analysis of our netlist clustering on Ariane NanGate45 benchmark, with the DBI values indicated. Densities and proximity of clusters are maintained despite their rearrangement.
  • Figure 3: Noticeable shift in cell density between global and post-route stages on the BlackParrot NanGate45 benchmark, with the post-route density providing more valuable information into later-stage timing and congestion optimizations.
  • Figure 4: (a) The Quantile-Quantile plot of the density of one cell across the Pareto-optimal placements follows a Gaussian distribution. (b) Using the empirical Bayes James-Stein estimator on the Ariane ASAP7 benchmark to learn optimal cell density targets $\boldsymbol{\hat{\mu}^{(\mathrm{JS})}}$ (green) by shrinking the tool distribution $\boldsymbol{z}$ (blue) towards achievable prior densities of DREAMPlace $\boldsymbol{\hat{\mu}^{(\mathrm{P})}}$ (yellow).
  • Figure 5: Cell density map and overlaid horiz./vert. congestion maps on the Ariane NanGate45 design. The density modulation through cell inflation eliminates the hotspot, resulting in enhanced congestion metrics: (a) peak-weighted-congestion (PWC)=0.85, max/tot. overflow=0.07/0.34 (%); (b) PWC=0.77, max/tot. overflow 0.04/0.20 (%).
  • ...and 2 more figures

Theorems & Definitions (1)

  • theorem 1