Given a set of points P in the plane and using the rectilinear distance, some points of view related to the classical problem of finding its shortest spanning tree are considered. First, the main properties of Steiner trees are reviewed, next, an upper bound is obtained for the length of any shortest spanning tree forma set P enclosed in a square of one unit side. Finally, a backtracking-based algorithm is developed which allows to find-when existing-a minimum-distance rectangle tree for any distribution P. These rectangle trees simplifies very much the task of looking for a Steiner tree. In fact, they allow the Steiner Tree Problem to become resoluble using a polynomial-time algorithm.
