On Solving Simple Curved Nonograms

Nonograms are a popular type of puzzle, where an arrangement of curves in the plane (in the classic version, a rectangular grid) is given together with a series of hints, indicating which cells of the subdivision are to be colored. The colored cells yield an image. Curved nonograms use a curve arrangement rather than a grid, leading to a closer approximation of an arbitrary solution image. While there is a considerable amount of previous work on the natural question of the hardness of solving a classic nonogram, research on curved nonograms has so far focused on their creation, which is already highly non-trivial. We address this gap by providing algorithmic and hardness results for curved nonograms of varying complexity.