Theory of linear and integer programming
Theory of linear and integer programming
Sets uniquely determined by projections on axes II Discrete case
Discrete Mathematics
Three-Dimensional Statistical Data Security Problems
SIAM Journal on Computing
Binary vectors partially determined by linear equation systems
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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
On the algorithmic inversion of the discrete Radon transform
Theoretical Computer Science
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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
On Stability, Error Correction, and Noise Compensation in Discrete Tomography
SIAM Journal on Discrete Mathematics
SIAM Journal on Discrete Mathematics
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
Feedback arc set in bipartite tournaments is NP-complete
Information Processing Letters
On the reconstruction of binary and permutation matrices under (binary) tomographic constraints
Theoretical Computer Science
Graph Theory
Linear Programming Based Approximation Algorithms for Feedback Set Problems in Bipartite Tournaments
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Stability in Discrete Tomography: some positive results
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
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DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
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Discrete tomography is concerned with the retrieval of finite point sets in some $\mathbbm{R}^d$ from their X-rays in a given number $m$ of directions $u_1,\ldots, u_m$. In the present paper we focus on uniqueness issues. The first remark gives a uniform treatment and extension of known uniqueness results. In particular, we introduce the concept of $J$-additivity and give conditions when a subset $J$ of possible positions is already determined by the given data. As a by-product, we settle a conjecture of Brunetti and Daurat on planar lattice convex sets. Remark 2 resolves a problem of Kuba posed in 1997 on the uniqueness in the case $d=m=3$ with $u_1,u_2,u_3$ being the standard unit vectors. Remark 3 determines the computational complexity of finding a smallest set $J$ of positions whose disclosure yields uniqueness. As a corollary, we obtain a hardness result for $0$-$1$-polytopes.