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We are interested in embedding trees T with maximum degree at most four in arectangular grid, such that the vertices of T correspond to grid points, whileedges of T correspond to non-intersecting straight segments of the grid lines.Such embeddings are called straight models. While each edge is represented by astraight segment, a path of T is represented in the model by the union of thesegments corresponding to its edges, which may consist of a path in the modelhaving several bends. The aim is to determine a straight model of a given treeT minimizing the maximum number of bends over all paths of T. We provide aquadratic-time algorithm for this problem. We also show how to constructstraight models that have k as its minimum number of bends and with the leastnumber of vertices possible. As an application of our algorithm, we provide anupper bound on the number of bends of EPG models of graphs that are both VPTand EPT.

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