Decomposing Rectilinear Figures into Rectangles

We discuss the problem of decomposing rectilinear regions, with or without holes, into a minimum number of rectangles. There are two different problems considered here: decomposing a figure into non-overlapping parts, called partitioning, and decomposing a figure into possibly overlapping parts, called covering. A method is outlined and proved for solving the above two problems, and algorithms for the solutions of these problems are presented. The partitioning problem can be solved in time O(n-to the 5/2), where n is the number of vertices of the figure, whereas the covering problem is exponential in its time complexity.