How to make a picturesque maze

In the picturesque maze generation problem, we are given a rectangular black-and-white raster image and want to randomly generate a maze in which the solution path fills up the black pixels. While a simple formulation of the problem faces with NP-hardness, the proposed method generates such a maze in polynomial time by appropriately changing the formulation itself. Therefore, the algorithm itself is quite simple. Figure 1: An example of a picturesque maze. (Up) A given black-and-white raster image. (Middle) An output, where two green rhombi represent the entrance and the exit. (Down) Showing that the solution path gives the input image. ∗Graduate School of Information Science and Engineering, Tokyo Institute of Technology, [email protected] †Supported by Global COE Program “Computationism as a Foundation for the Sciences” and Grant-in-Aid for Scientific Research from Ministry of Education, Science and Culture, Japan, and Japan Society for the Promotion of Science. ‡School of Information Science, Japan Advanced Institute of Science and Technology, [email protected]