No abstract

No abstract

No 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.

This paper presents several important enhancements to the recently published multilevel placement package mPL [12]. The improvements include (i) unconstrained quadratic relaxation on small, noncontiguous subproblems at every level of the hierarchy; (ii) improved interpolation (declustering) based on techniques from algebraic multigrid (AMG), and (iii) iterated V-cycles with additional geometric information for aggregation in subsequent V-cycles. The enhanced version of mPL, named mPL2, improves the total wirelength result by about 12% compared to the original version. The attractive scalability properties of the mPL run time have been largely retained, and the overall run time remains very competitive. Compared to gordian-l-domino [25] on uniformcell-size IBM/ISPD98 benchmarks, a speed-up of well over 8× on large circuits (≥ 100, 000 cells or nets) is obtained along with an average improvement in total wirelength of about 2%. Compared to Dragon [32] on the same benchmarks, a speed-up of about 5× is obtained at the cost of about 4% increased wirelength. On the recently published PEKO synthetic benchmarks, mPL2 generates surprisingly high-quality placements -roughly 60% closer to the optimal than those produced by Capo 8.5 and Dragon -in run time about twice as long as Capo's and about 1/10th of Dragon's.