Tiling Under Tomographic Constraints: A Note on Reconstruction

Title: Tiling Under Tomographic Constraints: A Note on Reconstruction

Research Question: How can we reconstruct a tiling from its projections, given a set of tiles with specific shapes?

Methodology: The researchers used a combination of combinatorial analysis and computer simulations to study the problem of reconstructing a tiling from its projections. They focused on tiles that are hole-less polyominoes, which are shapes that can be formed by placing tiles together without any gaps.

Results: The researchers proved that the problem of reconstructing a tiling from its projections is NP-complete for certain sets of tiles. This means that the problem is computationally difficult and it is unlikely that an efficient algorithm can be found to solve it for all possible sets of tiles.

Implications: The results of this study have implications for the field of discrete tomography, which involves reconstructing discrete objects from their projections. The study provides a better understanding of the complexity of this problem and may lead to the development of more efficient algorithms for specific cases. Additionally, the study contributes to the ongoing research in combinatorial analysis and computer science.

Link to Article: https://arxiv.org/abs/0108010v3 Authors: arXiv ID: 0108010v3