A strongly polynomial algorithm to solve combinatorial linear programs
Operations Research
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
Sets uniquely determined by projections on axes II Discrete case
Discrete Mathematics
Three-Dimensional Statistical Data Security Problems
SIAM Journal on Computing
The discrete Radon transform and its approximate inversion via linear programming
Discrete Applied Mathematics
On the computational complexity of reconstructing lattice sets from their x-rays
Discrete Mathematics
The reconstruction of binary patterns from their projections
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Reconstruction of Finite Lattice Sets from their X-Rays
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
Analysis on the strip-based projection model for discrete tomography
Discrete Applied Mathematics
On the reconstruction of binary and permutation matrices under (binary) tomographic constraints
Theoretical Computer Science
Additivity obstructions for integral matrices and pyramids
Theoretical Computer Science
Uniqueness in Discrete Tomography: Three Remarks and a Corollary
SIAM Journal on Discrete Mathematics
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The present paper deals with the computational complexity of the discrete inverse problem of reconstructing finite point sets and more general functionals with finite support that are accessible only through some of the values of their discrete Radon transform. It turns out that this task behaves quite differently from its well-studied companion problem involving 1-dimensional X-rays. Concentrating on the case of coordinate hyperplanes in Rd and on functionals :ZdD with D{{0,1,...,r},N0} for some arbitrary but fixed r, we show in particular that the problem can be solved in polynomial time if information is available for m such hyperplanes when md1 but is NP-hard for m=d and D={0,1,...,r}. However, for D=N0, a case that is relevant in the context of contingency tables, the problem is still in P. Similar results are given for the task of determining the uniqueness of a given solution and for a related counting problem.