Reconstructing permutation matrices from diagonal sums
Theoretical Computer Science
On the algorithmic inversion of the discrete Radon transform
Theoretical Computer Science
Discrete Tomography: Reconstruction under Periodicity Constraints
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
The Reconstruction of Some 3D Convex Polyominoes from Orthogonal Projections
SOFSEM '02 Proceedings of the 29th Conference on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
Stability and Instability in Discrete Tomography
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Reconstruction of Discrete Sets from Three or More X-Rays
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
An Algorithm for Reconstructing Special Lattice Sets from Their Approximate X-Rays
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Stability and instability in discrete tomography
Digital and image geometry
Privacy in multidimensional databases
Multidimensional databases
Random generation of 2×2×...×2×Jcontingency tables
Theoretical Computer Science
Stability results for the reconstruction of binary pictures from two projections
Image and Vision Computing
Statistical confidentiality: Optimization techniques to protect tables
Computers and Operations Research
On the reconstruction of binary and permutation matrices under (binary) tomographic constraints
Theoretical Computer Science
Graphs of transportation polytopes
Journal of Combinatorial Theory Series A
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Markov bases of three-way tables are arbitrarily complicated
Journal of Symbolic Computation
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Solving the two color problem: an heuristic algorithm
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Entry uniqueness in margined tables
PSD'06 Proceedings of the 2006 CENEX-SDC project international conference on Privacy in Statistical Databases
Discrete Optimization
A generalization of the integer linear infeasibility problem
Discrete Optimization
Uniqueness in Discrete Tomography: Three Remarks and a Corollary
SIAM Journal on Discrete Mathematics
On the non-additive sets of uniqueness in a finite grid
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
On the degree sequences of uniform hypergraphs
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Discrete tomography for inscribable lattice sets
Discrete Applied Mathematics
| Hi-index | 0.00 |
Suppose there is a three-dimensional table of cross-tabulated nonnegative integer statistics, and suppose that all of the row, column, and "file" sums are revealed together with the values in some of the individual cells in the table. The question arises as to whether, as a consequence, the values contained in some of the other (suppressed) cells can be deduced from the information revealed. The corresponding problem in two dimensions has been comprehensively studied by Gusfield [SIAM J. Comput., 17 (1988), pp. 552--571], who derived elegant polynomial-time algorithms for the identification of any such "compromised" cells, and for calculating the tightest bounds on the values contained in all cells that follow from the information revealed. In this note it is shown, by contrast, that the three-dimensional version of the problem is NP-complete. It is also shown that if the suggested row, column, and file sums for an unknown three-dimensional table are given, with or without the values in some of the cells, the problem of determining whether there exists any table with the given sums is NP-complete. In the course of proving these results, the NP-completeness of some constrained Latin square construction problems, which are of some interest in their own right, is established.