Symmetry-aware analog layout placement design handling substrate-sharing constraints

This paper presents a solution to handling the symmetry and substrate-sharing constraints in the placement design using transitive closure graph (TCG) representation for analog layouts. We propose a new contour-based packing scheme to implement substrate-sharing constraints with the time complexity of 0(p • n • lgn), where p is the number of symmetry groups and « is the number of the placed cells. Furthermore, a set of perturbation operations are devised with the time complexity of 0(n) in order to generate a new random symmetric-feasible TCG state. Our experimental results show the effectiveness of this approach compared to other competitive placement algorithms.