Reconstructing an alternate periodical binary matrix from its orthogonal projections

Authors:
Marie-Christine Costa;Fethi Jarray;Christophe Picouleau
Affiliations:
Laboratoire CEDRIC, Paris, France;Laboratoire CEDRIC, Paris, France;Laboratoire CEDRIC, Paris, France
Venue:
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Year:
2005

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Abstract

This paper deals with the reconstruction of an alternate periodical binary matrix from its orthogonal projections. For a fixed vector (p,q), a binary matrix A is alternate periodical when A$_{i,{\it j}}$+A$_{i+{\it p},{\it j}+{\it q}}$=1. For vectors (p = 1,q = 1),(p,0) and (0,q) we propose polynomial time algorithms to reconstruct an alternate periodical binary matrix from both its vertical and horizontal projections if such a matrix exists.