B*-Trees

We present in this paper an efficient, flexible, and effective data structure, B*-trees for non-slicing floorplans. B*-trees are based on ordered binary trees and the admissible placement presented in [1]. Inheriting from the nice properties of ordered binary trees, B*-trees are very easy for implementation and can perform the respective primitive tree, operations search, insertion, and deletion in only O(1), O(1), and O(n) times while existing representations for non-slicing floorplans need at least O(n) time for each of these operations, where n is the number of modules. The correspondence between an admissible placement and its induced B*-tree is 1-to-1 (i.e., no redundancy); further, the transformation between them takes only linear time. Unlike other representations for non-slicing floorplans that need to construct constraint graphs for cost evaluation, in particular, the evaluation can be performed on B*-trees and their corresponding placements directly and incrementally. We further show the flexibility of B*-trees by exploring how to handle rotated, pre-placed, soft, and rectilinear modules. Experimental results on MCNC benchmarks show that the B*-tree representation runs about 4.5 times faster, consumes about 60% less memory, and results in smaller silicon area than the O-tree one [1]. We also develop a B*-tree based simulated annealing scheme for floorplan design; the scheme achieves near optimum area utilization even for rectilinear modules.