Floorplanning using a tree representation a summary

Abstract

We present an ordered tree (O-tree) structure to represent nonslicing 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 directions. 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/sup 2n-2//n/sup 1.5/). This is very concise compared to a sequence pair representation that has O((n!) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) combinations. The approximate ratio of sequence pair and O-tree combinations is O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (n/4e)/sup n/). The complexity of an O-tree is even smaller than a binary tree structure for a slicing floorplan that has O(n!2/sup 5n-3//n/sup 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 (www.mcnc.org) benchmarks show promising performance with average 16% improvement in wire length and 1% less dead space over the previous central processing unit (CPU) intensive cluster refinement method.