Minimum Number of Bends of Paths of Trees in a Grid Embedding

We are interested in embedding trees T with ∆(T) ≤ 4 a rectangular grid, such that the vertices of correspond to grid points, while edges non-intersecting straight segments lines. Such embeddings called models. While each edge is represented by segment, path model union corresponding its edges, which may consist having several bends. The aim determine given tree minimizing maximum number bends over all paths T. provide quadratic-time algorithm for this problem. also show how construct models have k as minimum and least possible. As an application our algorithm, we upper bound on EPG VPT ∩ EPT graphs.