Floorplanning via graph dualization with subsets of rectangular and L-shaped modules

The graph dualization approach to floorplan design starts from an undirected graph representing the adjacency relations among modules, and then finds a dissection of a rectangle into rectilinear regions such that the modules and regions have a one-to-one correspondence and that the adjacency requirements are satisfied. Necessary and sufficient conditions are presented for a n-vertex graph G with two vertex subsets V_R and V_L to admit an R-L dual where a dissection of a rectangle into n rectilinear regions is such that each vertex of V_R ( V_L) corresponds to a rectangular (L-shaped) region. Generally, G can be tested in O(n²) time whether or not it has an R-L dual, and if one exists, it can be constructed in O(n) time