Par-POPINS: a timing-driven parallel placement method with the Elmore delay model for row based VLSIs

Abstract

In this paper, we present a parallel algorithm running on a shared memory multi-processor workstation for timing driven standard cell layout. The proposed algorithm is based on POPINS2.0 [13] and consists of three phases. First, we get an initial placement by a hierarchical timing-driven mincut placement algorithm. At the top level of partitioning hierarchy, we perform one step of bi-partitioning by several processors, and in the lower levels of partitioning hierarchy, partitionings of each region in a level are performed in parallel. Next, in phase 2, iterative improvement of the sub-circuit which contains critical paths is performed by nonlinear programming. Parallel processing is realized by performing the nonlinear programming method to each sub-circuit in parallel. Finally, in phase 3, the placement is transformed to a row based layout style by a timing-driven row assignment method. We have implemented the proposed method on a 4CPU multi-processor workstation and showed that the proposed method is promising through experimental results. I INTRODUCTIONIn recent years, performance of integrated circuits becomes higher and operation speed of logic circuits becomes faster.Hence, for high performance VLSI chips, the interconnection delay is much longer than the gate delay, and it is a major part of whole signal delay of chips. Therefore timing-driven layout methods which take interconnection delay into account explicitly, have been urged to be developed.There have been many studies about timing-driven placement, and they can be classified into the following four approaches, (1) the net weighting approach [l, 3,15,17,20], (2) the net delay bounds approach [6,9,10, 16,211, (3) the path weighting approach [8,22], and (4) the path delay bounds approach [2,7,11,12,19]. However, many of them have a difficulty of trade-off between the quality of the layout and the computation time. Especially for interconnection delay, the estimation of the interconnection delay is inaccurate because of some simplified assumptions of the delay model. Then, we have proposed a timing-driven placement method, called POPINS2.0 [13], which is based on the path delay bounds approach and adopted the delay estimation model based on Elmore's delay model. Experimental results have showed the effectiveness of POPINS2.0. However, in the case of VLSIs which have so much cells in one chip, the computation time of this placement method increased, because of the iterative improvement phase based on nonlinear programming and the row assignment phase based on linear assignment.In this paper, we propose a parallel algorithm for timingdriven placement, which is an extension of POPINS2.0. To obtain high efficiency of parallel processing, we restrict the amount o f communication among processors as much as possible by partitioning the placement problem into some subproblems which can be executed independently. The proposed algorithm consists of three phases. First, we get an initial placement by a hierarchical timing-drivcn mincut placement algorithm. At th...

Parallel standard cell placement on a cluster of workstations

“…These two benchmarks also did not achieve good speedup despite their large size. We are currently looking more closely at their behavior to try to gain insight into their behavior; other studies report difficulties with these benchmarks [21]. The reduction in quality is significantly smaller than that reported in other parallel placement studies.…”

“…The reduction in quality is significantly smaller than that reported in other parallel placement studies. For example, in one study the quality degradation of the parallel solution reached 30% (with an average of 14%) [21] on a 4 processor study. In another study, the quality drop also reached over 30% with an average of around 20%.…”

“…Because of the computational complexity of placement, there has been significant interest in parallelizing placement algorithms since the 1980's (see for example [8,16,19,20,21,22,24]; a good summary is available here [2]). These studies have experimented with parallelizing most of the placement algorithms on a variety of parallel architectures.…”

“…The speedup across different implementations were reported on the ISCAS benchmarks. Koide et al present a parallel implementation of their POPINS timing driven placement tool [21]. They use a bisection approach similar to our own, with non-linear programming used in a second phase optimization.…”

Min-max placement for large-scale timing optimization

“…9 In addition, several other interconnect length estimations can be used, such as a weighted half-perimeter wirelength [2], the length of a minimum single-trunk Steiner tree or the length of a heuristic Rectilinear Steiner Minimum Tree (RSMT). 10 To better model delays, the functions d i j could also depend on locations of cells (topologically) adjacent to i and j [18]. slack maximization is a special case of min Φ.…”