Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Straight line embeddings of cubic planar graphs with integer edge lengths
Journal of Graph Theory
Area-universal rectangular layouts
Proceedings of the twenty-fifth annual symposium on Computational geometry
On rectilinear duals for vertex-weighted plane graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
Point-set embeddings of plane 3-trees
GD'10 Proceedings of the 18th international conference on Graph drawing
Improved algorithms for the point-set embeddability problem for plane 3-trees
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Embedding stacked polytopes on a polynomial-size grid
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Linear-time algorithms for hole-free rectilinear proportional contact graph representations
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Drawing planar 3-trees with given face areas
Computational Geometry: Theory and Applications
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We study straight-line drawings of planar graphs such that each interior face has a prescribed area. It was known that such drawings exist for all planar graphs with maximum degree 3. We show here that such drawings exist for all planar partial 3-trees, i.e., subgraphs of a triangulated planar graph obtained by repeatedly inserting a vertex in one triangle and connecting it to all vertices of the triangle. Moreover, vertices have rational coordinates if the face-areas are rational, and we can bound the resolution. We also give some negative results for other graph classes.