Visibility Representations of Trees

摘要

Trees are among the most common structures in computing and many algorithms fordrawing trees have been developed in the last years. Such algorithms usually adopt different drawing conventions and attempt to solve several optimization problems. The aim of this paper is to study two different types of drawing conventions for trees, namely 1-strong visibility representation and 2-strong visibility representation. For both of them we investigate the problem of minimizing the area of the representation. The contribution of the paper is twofold: (1) we prove tight lower and upper bounds on the area of such representations; and (2) we provide linear-time algorithms that construct representations with optimal area.