Effectively Labeling Planar Projections of Polyhedra

A well-known method for interpreting planar projections (images) of 3-dimensional polyhedra is to label their lines by the Clowes-Huffman scheme. However, the question of whether there is such a labeling has been shown to be NP-complete. In this paper, a linear in time algorithm is given that answers the labelability question under the assumption that some information is known about those edges of the polyhedron whose both faces are visible. In many cases, this information can be derived from the image itself. Moreover, the algorithm has an effective parallel version, i.e., with polynomially many processors it can be executed in time polynomial in log n.