Typical placement objectives involve reducing net-cut cost or minimizing wirelength. Congestion minimization is least understood, however, it models routability accurately. In thii paper, we study the congestion minimization problem during placement. We introduce the notion of consistent routing model and promote its adoption by placement systems. First, we show that in thii model the wirelength objective is indeed a good measure of congestion by establishing that a placement with minimum wirelength has minimum total congestion. We show that miniibmg wirelength may (and in general, will) create locally congested regions. We demonstrate that most other congestion related objectives are ill behaved and they should only be used in a post processing step. We then propose several novel congestion minimization objectives. One in psrticulsr, called overflow minimization with look-ahead, performs very well and can be computed very efficiently in an incremental manner. At the end, we propose a post processing phase that further improves the congestion. By combining the overflow minimization with look-ahead and the post processing phase, we improve the congestion by more than 40% on the average.
As technology advances, more and more issues need to be considered in the placement stage, e.g., wirelength, congestion, timing, coupling. It is very hard to consider all of them together at the same time. Thus it is good if we can optimize one cost function without affecting others. In this paper, we will study methods to optimize congestion in placement without inflicting degradations/violations in other objectives or constraint. We give a mathematical equation to predict the overflow within a region using a normal distribution approximation. According to experiments, this equation does give a good estimation of overflow. We used this equation to find the smallest regions which have enough routing resource to alleviate the congestion and propose the flexible expansion scheme in our multi-center congestion reduction (MC'R) algorithm. Experimental results show that generally there is a correlation between the amount of reduction in congestion and the amount of change made to the placement: the more we change the placement, the more reduction in congestion we will get. However, the flexible expansion scheme is very effective in helping us reduce congestion while make only little change to the placement. Comparing to the full expansion scheme (49% congestion reduction and 6.5% change in placement), the flexible expansion scheme together with MC'R algorithm can reduce congestion by almost the same amount (42%) with much less change made to the placement (1.8%).
Abstract| Typical placement objectives involve reducing net-cut cost or minimizing wirelength. Congestion minimization is least understood, however, it models routability most accurately. In this paper, we study the congestion minimization problem during placement. First we pointed out that the bounding box router used in 12 is not an accurate measurement of the congestion in the placement. We use a realistic global router to evaluate congestion in the placement stage. This ensures that the nal placement is truely congestion minimized. We also proposed two new post processing algorithms, the ow-based cell-centric algorithm and the net-centric algorithm. While the ow-based cell-centric algorithm can move multiple cells at the same time to minimize the congestion, it su ers large consumption of memory. Experimental results show that the net-centric algorithm can e ectively identify the congested spots in the placement and reduce the congestion. It can produce on an average 7:7 less congestion than the method proposed in 12 . Finally, we use a nal global router to verify that the placement obtained from our algorithm has 39 less congestion than a wirelength-optimized placement obtained by TimberWolf commercial version 1.3.1.
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