A Robust Newton-type Iteration Method for Mixed-Cell-Height Legalization

The development of advanced technology nodes has led to a tendency toward mixed-cell-height layouts, which increases the complexity of the design. In this paper, a robust Newton-type (RN) iteration method is proposed to address the mixed-cell-height legalization problem. First, the legalization problem is modeled as a quadratic programming (QP) problem. Then the QP problem is transformed into a linear complementarity problem (LCP). By restating a pair of nonnegative orthogonal vectors in the LCP, the LCP is further converted into a generalized absolute value equation (GAVE). Considering that the system matrix
$Q$
in the LCP is positive semi-definite, to make sure that the system matrix is well-defined when solving the equivalent GAVE, we perturb
$Q$
to make it a positive definite matrix so that the generalized Newton iteration method can be effectively applied to the legalization problem. Further, we discuss the sufficient conditions for the RN method to be well-defined and convergent. Compared with the state-of-the-art works, the experimental results verify the efficiency and robustness of the proposed method.