Year: 2025
Type: preprint
Abstract: A well-known result by Kant [Algorithmica, 1996] implies that $n$-vertex outerplane graphs admit embedding-preserving planar straight-line grid drawings where the internal faces are convex polygons in $O(n^{2})$ area. In this paper, we present an algorithm to compute such drawings in $O(n^{1.5})$ area. We also consider outerplanar drawings in which the internal faces are required to be strictly-convex polygons. In this setting, we provide a $Θ(nk^2)$ area bound for $n$-vertex outerplanar graphs whose weak dual is a path and whose maximum face size is $k$ and a $Θ(nd^2)$ area bound for $n$-vertex outerplanar graphs whose diameter is bounded by $d$.
Source: arXiv (Cornell University)
Language: English
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7078600217
Cites:
Cited by:
Related to: