Phylogenetic trees or evolutionary trees show the evolutionary relationship among various biological species. In rooted trees the edge length between an ancestor and its descendants can represent the time, or sometimes genetic distance, between them. We study the problem of constructing an upward planar orthogonal drawing of a tree in which the vertical length of each edge is fixed and the goal is to minimize the width of the drawing. We show that even for binary trees this is NP-hard, but if the ordering of the children is fixed then it can be resolved in polynomial time. Finally we provide a heuristic algorithm for solving it with good width in practice (work in progress).
(Joint work with Michael T. Goodrich, Timothy Johnson, and Martha Osegueda.)