POLAR: Placement based on novel rough legalization and refinement

Abstract

Abstract-A new quadratic global placer called POLAR is proposed. POLAR is based on novel techniques for rough legalization and wirelength refinement. During look-ahead rough legalization (LAL), relative positions of cells are maintained as they are relocated with minimal displacement to relieve excess area density. For each "hotspot" where placement overfill occurs, an expansion region covering the hotspot is constructed. Then the movable cells within each of these expansion regions are evenly assigned to density bins inside the expansion region by displacement-minimizing recursive bisection. In addition, a fast density-preserving and wirelength-reducing discrete refinement is applied to the first few LAL placements before each of these is used to augment the quadratic model used to obtain the next major placement iteration. The experimental results show that POLAR outperforms the state-of-the-art academic placers over the ISPD 2005 benchmarks.

ePlace-MS: Electrostatics-Based Placement for Mixed-Size Circuits

“…The electrostatic equilibrium state is coupled with even placement density distribution and will be eventually reached. Compared to all the previous mixed-size placement algorithms [3], [13], [15], [17], [21], [39], [46], [47], our density function achieves the minimum density overflow as shown in Table III, indicating the fewest violations to the target density thus the best performance of our density function.…”

“…(2) in order to achieve analyticity. Modern quadratic placers [17], [18], [21], [45], [46] are all based on the density force formulation proposed in [7], where anchor points are inserted to drag cells away from over-filled region, modeling the density force as a constant term in the gradient function. In contrast, nonlinear placers formulate the density gradient as a component independent to wirelength.…”

“…One-stage solution remains popular among most modern placement algorithms [13], [15], [17], [18], [21], [46]. Macros and standard cells are being placed simultaneously where the limitations discussed above can be well avoided.…”

Placement: From Wirelength to Detailed Routability

“…POLAR 2.0 [45] proposes a routability-driven rough legalization, which extends its previous work of Ref. [53] with consideration of routing congestion. In the original work, placement density hotspots are identified as local regions with cell area density exceeding the target density.…”

A Connectivity-Based Legalization Scheme for Standard Cell Placement

“…Gordian [7] utilizes the connectivity between cells in the direction of formulating a series of quadratic programming problems, by iteratively partitioning the available area and adding new constraints that restrict cell movement, whilst recalibrating each cell's position to obtain the minimum wirelength. FastPlace3 [8] focuses on improving the overall runtime in the expense of the final solution quality, and POLAR [9] achieves speedup by applying parallelization techniques throughout the execution of the problem's formulation and solution procedures.…”