This paper presents a solution to handling complex multi-group 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 automatically satisfy symmetry requirements. We also develop a new contour-based packing scheme with time complexity of O(g÷n÷lgn), where g is the number of symmetry groups and n is the number of the placed cells. Furthermore, we devise a set of perturbation operations with time complexity of O(n). Our experimental results show the effectiveness and superiority of this proposed scheme compared to the other state-of-the-art placement algorithms for analog layout design.
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