A linear-time algorithm for drawing a planar graph on a grid
Information Processing Letters
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Linear-time computability of combinatorial problems on series-parallel graphs
Journal of the ACM (JACM)
Drawing Outer-Planar Graphs in O(n log n) Area
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
A Lower Bound on the Area Requirements of Series-Parallel Graphs
Graph-Theoretic Concepts in Computer Science
Small Area Drawings of Outerplanar Graphs
Algorithmica
A note on minimum-area straight-line drawings of planar graphs
GD'07 Proceedings of the 15th international conference on Graph drawing
Small drawings of series-parallel graphs and other subclasses of planar graphs
GD'09 Proceedings of the 17th international conference on Graph Drawing
Small grid drawings of planar graphs with balanced bipartition
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Universal point sets for planar three-trees
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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In a grid drawing of a planar graph, every vertex is located at a grid point, and every edge is drawn as a straight-line segment without any edge-intersection. It is known that every planar graph G of n vertices has a grid drawing on an (n驴2)脳(n驴2) or (4n/3)脳(2n/3) integer grid. In this paper we show that if a planar graph G has a balanced partition then G has a grid drawing with small grid area. More precisely, if a separation pair bipartitions G into two edge-disjoint subgraphs G 1 and G 2, then G has a max驴{n 1,n 2}脳max驴{n 1,n 2} grid drawing, where n 1 and n 2 are the numbers of vertices in G 1 and G 2, respectively. In particular, we show that every series-parallel graph G has a (2n/3)脳(2n/3) grid drawing and a grid drawing with area smaller than 0.3941n 2 (2 n 2).