Arbitrary convex and concave rectilinear block packing based on O-Tree representation

In this paper, we propose an improved method to represent rectilinear block packing based on O-Tree representation. Also, we propose a decoding algorithm to obtain a rectilinear block packing in O((c+1)n) time, where n and c are the number of rectangular sub-blocks and concave blocks respectively. Note that the proposed algorithm requires only O(n) time when c is constant, which is equal to the trivial lower bound of time complexity for decoding. The effectiveness of the proposed method was confirmed by the experimental comparisons.