Twin binary sequences

Abstract

The efficiency and effectiveness of many floorplanning methods depend very much on the representation of the geometrical relationship between the modules. A good representation can shorten the searching process so that more accurate estimations on area and interconnect costs can be performed. Non-slicing floorplan is the most general kind of floorplan that is commonly used. Unfortunately, there is not yet any complete and non-redundant topological representation for non-slicing structure. In this paper, we will propose the first representation of this kind. Like some previous work [9], we have also made used of mosaic floorplan as an intermediate step. However, instead of including a more than sufficient number of extra dummy blocks in the set of modules, our representation allows us to insert an exact number of irreducible empty rooms to a mosaic floorplan in such a way that every non-slicing floorplan can be obtained by this method uniquely from one and only one mosaic floorplan. The size of the solution space is only O(n!23n/n1.5) but every non-slicing floorplan can be generated uniquely and efficiently in linear time without any redundant representation.