Canonical embedding of rectangular duals with applications to VLSI floorplanning

The notion of equivalent embedding of rectangular duals is introduced, leading to a new concept of canonical embedding of a rectangular dual; this is a floorplan corresponding to a given neighborhood graph such that the number of directed cycles in its channel digraph is minimum. Strongly maximal rectangular hierarchy (sMRH) in nonslicible floorplans is then defined. The canonical form of any arbitrary floorplan consists of at most one nonslicing core for each member of sMRH. Such an embedding therefore represents a floorplan with minimum deviations from a slicing structure. An O(n ²) algorithm for realizing a canonical embedding is also presented. Canonical embedding lends deep insight to the yet unsolved problem of characterizing inherent nonslicibility and motivates design for slicibility. It also makes determination of safe routing order simple