Upward Planar Morphs
When
Tuesday, Sept 18th at 5:00 PM
Where
Department of Engineering
Section of Computer Science and Automation
Via della Vasca Navale, 79
Meeting room (1.10) on 1st floor
Speaker
Vincenzo Roselli
Postdoctoral Fellow
Roma Tre University
Abstract
We prove that, given two topologically-equivalent upward planar straight-line drawings of an n-vertex directed graph G, there always exists a morph between them such that all the intermediate drawings of the morph are upward planar and straight-line. Such a morph consists of O(1) morphing steps if G is a reduced planar st-graph, O(n) morphing steps if G is a planar st-graph, O(n) morphing steps if G is a reduced upward planar graph, and O(n^2) morphing steps if G is a general upward planar graph. Further, we show that Ω(n) morphing steps might be necessary for an upward planar morph between two topologically-equivalent upward planar straight-line drawings of an n-vertex path.
Joint work with Giordano Da Lozzo, Giuseppe Di Battista, Fabrizio Frati, and Maurizio Patrignani
