On the computational complexity of reconstructing lattice sets from their x-rays
Discrete Mathematics
On the comptational complexity of determining polyatomic structures by X-rays
Theoretical Computer Science
Reconstructing polyatomic structures from discrete X-rays: NP-completeness proof for three atoms
Theoretical Computer Science
Reconstruction of binary matrices under fixed size neighborhood constraints
Theoretical Computer Science
Note: A solvable case of image reconstruction in discrete tomography
Discrete Applied Mathematics
Using graphs for some discrete tomography problems
Discrete Applied Mathematics
On the degree sequences of uniform hypergraphs
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
A formulation of the wide partition conjecture using the atom problem in discrete tomography
Discrete Applied Mathematics
Solving Multicolor Discrete Tomography Problems by Using Prior Knowledge
Fundamenta Informaticae - Strategies for Tomography
| Hi-index | 5.23 |
In the field of Discrete Tomography, the 2-color problem consists in reconstructing a matrix whose elements are of two different types, starting from its horizontal and vertical projections. It is known that the 1-color problem admits a polynomial time reconstruction algorithm, while the c-color problem, with c=2, is NP-hard. Thus, the 2-color problem constitutes an interesting example of a problem just in the frontier between hard and easy problems. In this paper we define a linear time algorithm (in the size of the output matrix) to solve a subclass of its instances, where some values of the horizontal and vertical projections are constant, while the others are upper bounded by a positive number proportional to the dimension of the problem. Our algorithm relies on classical studies for the solution of the 1-color problem.