Big: A Bivariate Gradient-Based Wirelength Model for Analytical Circuit Placement

The analytical formulation has been shown to be the most effective for circuit placement. A key ingredient of analytical placement is its wirelength model, which needs to be differentiable and can accurately approximate a golden wirelength model such as half-perimeter wirelength. Existing wirelength models derive gradient from differentiating smooth maximum (minimum) functions, such as the log-sum-exp and weighted-average models. In this paper, we propose a novel bivariate gradient-based wirelength model, namely BiG, which directly derives a gradient with any bivariate smooth maximum (minimum) function without any differentialion. Our wirelength model can effectively combine the advantages of both multivariate and bivariate functions. Experimental results show that our BiG model effectively and efficiently improves placement solutions.