Grid straight-line embeddings of trees with a minimum number of bends per path

Abstract

A grid embedding of a tree T whose vertices have degree at most four is an embedding in which the vertices of T are represented by points with integer coordinates, and the edges are represented by interior-disjoint horizontal or vertical line segments joining pairs of adjacent vertices in T. In any such embedding, a path of T may bend several times. In this paper we obtain a linear-time algorithm that given a tree T finds a grid embedding of T that minimizes the maximum number of times any path of T bends. All of the results presented here generalize easily to lattice embeddings of trees in higher dimensions.