x-architecture placement based on effective wire models
In this paper, we derive the X-half-perimeter wirelength (XHPWL) model for X-architecture placement and explore the effects of three different wire models on X-architecture placement, including the Manhattan-half-perimeter wirelength (MHPWL) model, the XHPWL model, and the X-Steiner wirelength (XStWL) model. For min-cut partitioning placement, we propose a generalized net-weighting method that can exactly model the wirelength after partitioning by the net weight. The net-weighting method is general and can be incorporated into any wire models such as the XHPWL and XStWL models. For analytical placement, we smooth the XHPWL function using log-sum-exp functions to facilitate analytical placement. Our study shows that both the XHPWL model and the XStWL model can reduce the X wirelength. In particular, our results reveal the effectiveness of the X architecture on wirelength reduction during placement and thus the importance of the study on the X-placement algorithms, which is different from the results given in the previous work that the X-architecture placement might not improve the X-routing wirelength over the Manhattan-architecture placement.
placement partitioning net weighting x architecture steiner tree min cut physical design