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(n2) 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.
Da Lozzo, G., Di Battista, G., Frati, F., Patrignani, M., Roselli, V. (2018). Upward planar morphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp.92-105). Springer Verlag [10.1007/978-3-030-04414-5_7].
Upward planar morphs
Da Lozzo, Giordano;Di Battista, Giuseppe;Frati, Fabrizio;Patrignani, Maurizio;Roselli, Vincenzo
2018-01-01
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(n2) 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
