We present an ordered tree, O-tree, structure to represent non-slicing floor-plans. The O-tree uses only n (2 + rig nl) bits for a floorplan of n rectangular blocks.We define an admissible placement as a compacted placement in both x and y direction. For each admissible placement, we can find an O-tree representation. We show that the number of possible O-tree combinations is O(n. 2 1 " -2 I nl*'). This is very concise compared to a sequence pair representation which has O((n!)2) combinations. The approximate ratio of sequence pair and Otree combinations is O(n2 (n / 4e)"). The complexity of O-tree is even smaller than a binary-ree #ucture for slicing floorplan which has O(n! 2'In * ) combinations. Given an O-tree, it takes only linear time to construct the placement and its constraint graph. We have developed a deterministic floorplanning algorithm utilizing the structure of O-tree. Empirical results on MCNC benchmarks show promising performance with average 16% improvement in wire length, and 1% less in dead space over previous CPU-intensive cluster refinement method.

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The ordered tree (O-tree) representation has recently gained much interest in layout design automation. Different from previous topological representations of non-slicing floorplans, the O-tree representation is simpler, needs linear computation effort to generate a corresponding layout, and exhibits a smaller upper-bound of possible configurations. This paper addresses the problem of handling symmetry constraints in the context of the O-tree representation. This problem arises in analog placement, where symmetry is often used to match layout-induced parasitics and to balance thermal couplings in differential circuits. The good performance of our placement tool dealing with several analog designs taken from industry proves the effectiveness of our technique.