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

Abstract

We present an ordered tree, O-tree, structure to represent non-slicing floorplans. The O-tree uses only n (2 + ⎡lg 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 Otree combinations is O(n 2 (n /4e) n). The complexity of 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. 1.