An O-tree representation of non-slicing floorplan and its applications

We present an ordered tree, O-tree, structure to represent non-slicing floorplans. The O-tree uses only n(2+[Ig n]) 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! 2^2n-2/n^1.5). This is very concise compared to a sequence pair representation which has O((n!)2) combinations. The approximate ratio of sequence pair and O-tree combinations is O(n² (n/4e)ⁿ). The complexity of the O-tree is even smaller than a binary tree structure for slicing floorplan which has O(n! 2^5n-3/n^1.5) 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