Planar graph decomposition and all pairs shortest paths
Journal of the ACM (JACM)
Handbook of theoretical computer science (vol. A): algorithms and complexity
Handbook of theoretical computer science (vol. A): algorithms and complexity
Journal of Algorithms
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Drawing graphs: methods and models
Drawing graphs: methods and models
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Introduction to Algorithms
Straight-Line Drawings on Restricted Integer Grids in Two and Three Dimensions
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
Drawing Outer-Planar Graphs in O(n log n) Area
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Polynomial area bounds for MST embeddings of trees
Computational Geometry: Theory and Applications
Straight-line drawings of outerplanar graphs in O(dnlogn) area
Computational Geometry: Theory and Applications
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It is important to minimize the area of a drawing of a graph, so that the drawing can fit in a small drawing-space. It is well-known that a planar graph with n vertices admits a planar straight-line grid drawing with O(n^2) area [H. de Fraysseix, J. Pach, R. Pollack, How to draw a planar graph on a grid, Combinatorica 10(1) (1990) 41-51; W. Schnyder, Embedding planar graphs on the grid, in: Proceedings of the First ACM-SIAM Symposium on Discrete Algorithms, 1990, pp. 138-148]. Unfortunately, there is a matching lower-bound of @W(n^2) on the area-requirements of the planar straight-line grid drawings of certain planar graphs. Hence, it is important to investigate important categories of planar graphs to determine if they admit planar straight-line grid drawings with o(n^2) area. In this paper, we investigate an important category of planar graphs, namely, outerplanar graphs. We show that an outerplanar graph G with degree d admits a planar straight-line grid drawing with area O(dn^1^.^4^8) in O(n) time. This implies that if d=o(n^0^.^5^2), then G can be drawn in this manner in o(n^2) area.