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 . 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 . © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Chen, C. Y., Hung, Y. F., & Lu, H. I. (2009). Visibility representations of four-connected plane graphs with near optimal heights. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5417 LNCS, pp. 67–77). Springer Verlag. https://doi.org/10.1007/978-3-642-00219-9_8
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