Routability is one of the primary objectives in placement. There have been many researches on forecasting routing problems and improving routability in placement but no perfect solution is found. Most traditional routability-driven placers aim to improve global routing result, but true routability lies in detailed routing. Predicting detailed routing routability in placement is extremely difficult due to the complexity and uncertainty of routing. In this paper, we propose a new detailed routing routability prediction model based on supervised learning. After extracting key features in placement and detailed routing, multivariate adaptive regression is performed to train the connection between these two stages. Using a well-trained model, most design rule violations after detailed routing can be foreseen in placement stage. Experiments show that our average prediction accuracy is 79.8%, which is comparable with other state-of-art routability estimation techniques.

Routing congestion model is of great importance in design stages of modern physical synthesis, e.g. global routing and routability estimation during placement. As the technology node becomes smaller, routing congestion is more difficult to estimate during design stages ahead of detailed routing. In this paper, we propose a framework using nonparametric regression technique in machine learning to construct routing congestion model. The constructed model can capture multiple factors and enables direct prediction of detailed routing congestion with high accuracy. By using this model in global routing, significant reduction of design rule violations and detailed routing runtime can be achieved compared with the model in previous work, with small overhead in global routing runtime and memory usage. 1

With the rapid growth of design size and complexity, global routing has always been a hard problem. Several new factors contribute to global routing congestion and can only be measured and optimized in 3-D global routing rather than 2-D routing. We propose an enhanced congestion model in global routing to capture local congestion and more accurately reflect modern design rule requirements. To achieve better global and detailed routing solution quality, we propose a 3-D global router VFGR with parallel computing using this congestion model. Experimental results show that VFGR can achieve comparable or better global routing solution quality with two start-of-the-art global routers in shorter runtime. It is also demonstrated that adopting proposed congestion model in global routing, higher solution quality and much shorter runtime can be achieved in detailed routing stage.

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