Reconstructing hv-Convex Polyominoes from Orthogonal Projections
Abstract
Tomography is the area of reconstructing objects from projections. Here we wish to reconstruct a set of cells in a two dimensional grid, given the number of cells in every row and column. The set is required to be an hv-convex polyomino, that is all its cells must be connected and the cells in every row and column must be consecutive. A simple, polynomial algorithm for reconstructing hv-convex polyominoes is provided, which is several orders of magnitudes faster than the best previously known algorithm from Barcucci et al. In addition, the problem of reconstructing a special class of centered hv-convex polyominoes is addressed. (An object is centered if it contains a row whose length equals the total width of the object). It is shown that in this case the reconstruction problem can be solved in linear time.
Cite
@article{arxiv.cs/9906021,
title = {Reconstructing hv-Convex Polyominoes from Orthogonal Projections},
author = {Christoph Durr and Marek Chrobak},
journal= {arXiv preprint arXiv:cs/9906021},
year = {2007}
}