Visibility Representations of Four-Connected Plane Graphs with Near Optimal Heights

A visibility representation of a graph G is to represent the nodes of G with non-overlapping horizontal line segments such that the line segments representing any two distinct adjacent nodes are vertically visible to each other. If G is a plane graph, i.e., a planar graph equipped with a planar embedding, a visibility representation of G has the additional requirement of reflecting the given planar embedding of G. For the case that G is an n-node four-connected plane graph, we give an O(n)-time algorithm to produce a visibility representation of G with height at most n 2 + 2 n−2 2 . To ensure that the first-order term of the upper bound is optimal, we also show an n-node four-connected plane graph G, for infinite number of n, whose visibility representations require heights at least n 2 .

• Type: Conference
• Year: 2008
• Where: GD
• Authors: Chieh-Yu Chen, Ya-Fei Hung, Hsueh-I Lu
• Keywords: Computer Graphics, Four-connected Plane Graph, GD 2008, Plane Graph, Visibility Representations