On Solving Simple Curved Nonograms

TL;DR

This paper investigates the computational complexity of solving curved nonograms, a variant of puzzles involving curves instead of grids, providing new algorithmic and hardness results for these challenging problems.

Contribution

It offers the first comprehensive analysis of the complexity and algorithms for solving curved nonograms, extending understanding beyond traditional grid-based puzzles.

Findings

Established the computational hardness of solving curved nonograms.

Developed algorithms for certain classes of curved nonograms.

Identified complexity boundaries based on puzzle parameters.

Abstract

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.