Rectangular dualization and rectangular dissections

Rectangular dualization refers to finding a dual of a planar graph, that can be drawn in the form of a rectangular dissection; it has applications in architectural design and in the floorplanning of VLSI ICs. The authors present properties of rectangular dissections and discuss two related topics: (1) a problem of enumerating without repetitions all rectangular duals of a graph; and (2) transformations of rectangular dissections. The authors have developed a fast algorithm for enumerating rectangular duals that is based on a limited set of possible local changes in the structure of a rectangular dissection. A second procedure for systematically generating all rectangular duals of a graph is developed from the notion of partitioning the sets of rectangular dissections into disjoint subsets