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For rooted trees, an ideal drawing is one that is planar, straight-line, strictly-upward, and order-preserving. This paper considers ideal drawings of rooted trees with the objective of keeping the width of such drawings small. It is not known whether finding the minimum width is NPhard or polynomial. This paper gives a 2-approximation for this problem, and a 2∆-approximation (for ∆-ary trees) where additionally the height is O(n). For trees with ∆ ≤ 3, the former algorithm finds ideal drawings with minimum width. Submitted: August 2016 Reviewed: January 2017 Revised: February 2017 Accepted: April 2017 Final: April 2017 Published: April 2017 Article type: Regular paper Communicated by: G. Liotta Research supported by NSERC. E-mail address: biedl@uwaterloo.ca (Therese Biedl) 632 T. Biedl Ideal Tree-Drawings

Ideal Drawings of Rooted Trees With Approximately Optimal Width