Tiling Under Tomographic Constraints

Title: Tiling Under Tomographic Constraints

Research Question: How can we reconstruct a tiling of a grid given its projections, or determine if such a tiling exists?

Methodology: The researchers considered a 2D grid and tiles of different shapes. They defined projections, which are the counts of how many tiles of each type intersect each row and column. They then focused on the problem of reconstructing a tiling with given projections or determining if such a tiling exists.

Results: The researchers found that the complexity of reconstructing a tiling with given projections depends on the type of tiles and the constraints. They provided new results on the complexity of different variants of this problem.

Implications: These results contribute to the field of discrete tomography, which deals with reconstructing discrete objects from their projections. The findings can be applied in various fields such as computer science, mathematics, and physics, where problems involving tile-like structures and projections are common.

Link to Article: https://arxiv.org/abs/0108010v1 Authors: arXiv ID: 0108010v1