title: A Note on Minimum-Area Straight-line Drawings of Planar Graphs
creator: Frati, Fabrizio
creator: Patrignani, Maurizio
subject: G.070 Area / Edge Length
subject: P.720 Straight-line
description: Despite a long research effort, finding the minimum area for straight-line grid drawings of planar graphs is still an elusive goal. A long-standing lower bound on the area requirement for straight-line drawings of plane graphs was established in 1984 by Dolev, Leighton, and Trickey, who exhibited a family of graphs, known as nested triangles graphs, for which $(2n/3-1) times (2n/3-1)$ area is necessary. We show that nested triangles graphs can be drawn in $2n^2/9 + O(n)$ area when the outer face is not given, improving a previous $n^2/3$ area upper bound. Further, we show that $n^2/9 + Omega(n)$ area is necessary for any planar straight-line drawing of a nested triangles graph. Finally, we deepen our insight into the $4/9n^2-4/3n+1$ lower bound by Dolev, Leighton, and Trickey, which is conjectured to be tight, showing a family of plane graphs requiring more area.
publisher: Springer
contributor: Hong, Seok-Hee
contributor: Nishizeki, Takao
contributor: Quan, Wu
date: 2008
type: Conference Paper
type: NonPeerReviewed
identifier: Frati, Fabrizio and Patrignani, Maurizio (2008) A Note on Minimum-Area Straight-line Drawings of Planar Graphs. [Conference Paper]
relation: http://gdea.informatik.uni-koeln.de/856/