Linear time optimization of partially solved floorplans

Efficient optimization of floorplans is studied. For a given geometric figure (GF) which represents a partially solved floorplan, the problem of finding a realization in the form of a floorplan for which the enclosing rectangle has the minimum area and the adjacent cells touch one another along a side for at least one unit length is discussed. An O(n) time algorithm for finding a solution, if GF is fully triangulated, is provided. This result is extended to the case when the minimum horizontal and vertical lengths of cells and minimum contact requirements between cells are given. The linear-time algorithm can also be extended to provide channels of prescribed widths between adjacent cells. It is demonstrated that if certain adjacencies can be satisfied by contact through vacant rectangular areas, then the solution may not be optimal. A solution to this version of the problem is proposed. The difficulty of the problem when GF is not fully triangulated is explored, and an efficient heuristic algorithm for this version of the problem is provided. Extension to three-dimensional space-plan optimization is discussed