Three-Dimensional Statistical Data Security Problems
SIAM Journal on Computing
An Efficient Algorithm for Generating Necklaces with Fixed Density
SIAM Journal on Computing
A fast algorithm to generate necklaces with fixed content
Theoretical Computer Science
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
Reconstruction of binary matrices under fixed size neighborhood constraints
Theoretical Computer Science
The 1-color problem and the Brylawski model
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Realizing disjoint degree sequences of span at most two: A tractable discrete tomography problem
Discrete Applied Mathematics
A reconstruction algorithm for a subclass of instances of the 2-color problem
Theoretical Computer Science
SIAM Journal on Discrete Mathematics
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In hypergraph theory, determining a good characterization of d, the degree sequence of an h-uniform hypergraph $\mathcal{H}$, and deciding the complexity status of the reconstruction of $\mathcal{H}$ from d, are two challenging open problems. They can be formulated in the context of discrete tomography: asks whether there is a matrix A with nonnegative projection vectors H=(h,h,…,h) and V=(d1,d2,…,dn) with distinct rows. In this paper we consider the subcase where the vectors H and V are both homogeneous vectors, and we solve the related consistency and reconstruction problems in polynomial time. To reach our goal, we use the concepts of Lyndon words and necklaces of fixed density, and we apply some already known algorithms for their efficient generation.