Reconstructing convex polyominoes from horizontal and vertical projections II
In , we studied the problem of reconstructing a discrete set 5 from its horizontal and vertical projections. We defined an algorithm that establishes the existence of a convex polyomino Λ whose horizontal and vertical projections are equal to a pair of assigned vectors (H,V), with H ∈ ℕ m and V ∈ ℕ n . Its computational cost is O(n4m4). In this paper, we introduce some operations for recontructing convex polyominoes by means of vectors H's and V's partial sums. These operations allows us to define a new algorithm whose complexity is less than O(n2m2).
KeywordsConstruction Procedure Vertical Projection Adjacent Column Filling Operation Good Expansion
- 1.E. Barcucci, A. Del Lungo, M. Nivat and R. Pinzani, Reconstructing convex polyominoes from their horizontal and vertical projections, Theor. Comp. Sci. 155 (1996) 321–347.Google Scholar
- 2.M. R. Garey and D.S. Johnson, Computers and intractability: a guide to the theory of NP-completeness, Freeman, New York, (1979) 224.Google Scholar
- 3.G. J. Woeginger, The reconstruction of polyominoes from their orthogonal projections, (1996) Preprint.Google Scholar