Area-adaptive Drawing of Rooted Trees

When visually representing a rooted tree, a hierarchical drawing, a type of monotone drawing, is often used. In a layout where nodes with the same level are arranged on a horizontal straight line, the resulting shape often appears stretched horizontally. Depending on the aspect ratio of a rectangular drawing area, this can result in significant wasted space. This study presents a layout method developed to address this problem. The method maintains a monotone drawing but relaxes the criteria for arranging nodes with the same level on a horizontal straight line. Leaves with the same parent may be arranged on a folded line instead of a horizontal straight line; we call this a monotone local folding layout. Area adaptivity is introduced as a measure of spatial efficiency for a given drawing area, and the area adaptivity of the monotone local folding layout is investigated using 2500 randomly generated rooted trees as experimental data. This study also examines how area adaptivity is affected when the aspect ratio of the drawing area is changed. The experiments show that for rooted trees with many sibling leaves, the area adaptivity of the monotone local folding layout is good and is not affected by changes in the aspect ratio of the drawing area. As a result, the monotone local folding layout is an effective layout technique for rooted trees representing computer networks consisting of switches and many terminals.