Analog placement design with constraints of multiple symmetry groups

This paper presents a solution to handling multiple symmetry constraints in the placement design using transitive closure graph (TCG) representation for analog layouts. We propose a set of symmetric-feasible conditions, which can guarantee symmetric placement of sensitive cells with respect to multiple symmetry axes for reduction of parasitic mismatch and thermal gradients. We also develop a new contour-based packing scheme with time complexity of O(p-nlgn), where p is the number of symmetric groups and n is the number of the placed cells. Furthermore, a set of perturbation operations with time complexity of O(n), where n is the number of the placed cells, are defined in order to generate a random symmetric-feasible TCG configuration from an existing one. Our experimental results show the effectiveness of this approach compared to other state-of-the-art placement algorithms.