An Optimal Algorithm for Detecting Pseudo-squares

Srecko Brlek (1) , Xavier Provençal (1)

1 LaCIM - Laboratoire de combinatoire et d'informatique mathématique [Montréal]

We consider the problem of determining if a given word, which encodes the boundary of a discrete figure, tiles the plane by translation. These words have been characterized by the Beauquier-Nivat condition, for which we provide a linear time algorithm in the case of pseudo-square polyominoes, improving the previous quadratic algorithm of Gambini and Vuillon.

Domaines: Mathématique discrète [cs.DM]

Srecko Brlek, Xavier Provençal. An Optimal Algorithm for Detecting Pseudo-squares. Discrete Geometry for Computer Imagery, Oct 2006, Szeged, Hungary. pp.403-412, ⟨10.1007/11907350_34⟩. ⟨hal-00395242⟩