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Reconstructing hv-Convex Polyominoes from Orthogonal Projections

Christoph Durr·Marek Chrobak
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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.

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Christoph Durr, Marek Chrobak. 1999-06-22. Reconstructing hv-Convex Polyominoes from Orthogonal Projections. https://arxiv.org/abs/cs/9906021

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