Reconstruction of low-degree domino tilings

We want to present a new way of challenging the classical and still unsolved problem of the reconstruction of a domino tiling from its horizontal and vertical projections. We introduce the concept of degree of a domino tiling, i.e. we divide a domino tiling into strips-like sub-tilings and we consider the greatest of their heights. We propose an algorithm which generalizes some known strategies for reconstructing domino tilings of degree two, to tilings of degree lesser or equal four.