Tiling a simply connected figure with bars of length 2 or 3 Original Research Article

Let F be a simply connected figure formed from a finite set of cells of the planar square lattice. We first prove that if F has no peak (a peak is a cell of F which has three of its edges in the contour of F), then F can be tiled with rectangular bars formed from 2 or 3 cells. Afterwards, we devise a linear-time algorithm for finding a tiling of F with those bars when such a tiling exists.