An area minimizer for floorplans with L-shaped regions

Given a floorplan with L-shaped regions, the problem considered is to choose an implementation from a set of possible implementations for each module such that the resultant floorplan will have minimum area, subject to the constraint that the dual polar graphs of the floorplan must be preserved. The concept of a cut line is extended, and eight types of cut lines that are used to decompose floorplans with L-shaped regions are defined. An O(n³) time algorithm for deciding whether a given floorplan is decomposable is presented. A heuristic algorithm, which uses the cut tree obtained by the decomposition algorithm to solve the area minimization problem, is proposed. For floorplans that can not be decomposed by the decomposition algorithm, a branch-and-bound algorithm can be incorporated into the algorithm to solve the area minimization problem. The results obtained are superior to those obtained by running an existing mathematical programming package for at least 1 h, and the execution time is less than 3 min for the most complex test problem