Polyominoes defined by two vectors
Theoretical Computer Science
Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
The number of convex polyominoes reconstructible from their orthogonal projections
Proceedings of the 6th conference on Formal power series and algebraic combinatorics
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
Hi-index | 0.00 |
The problem of reconstructing a convex polyominoes from its horizontal and vertical projections when the projections are defined as the number of cells of the polyomino in the different lines and columns was studied by Del Lungo and M. Nivat. In this paper, we study the reconstruction of any convex polyomino when the orthogonal projections are defined as the contour length of the object intercepted by the ray. We prove the NP-hardness of this problem for several classes of polyominoes: general, h-convex, v-convex. For hv-convex polyominoes we give a polynomial time algorithm for the reconstruction problem.