Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Straight Line Embeddings of Planar Graphs on Point Sets
Proceedings of the 8th Canadian Conference on Computational Geometry
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On embedding an outer-planar graph in a point set
Computational Geometry: Theory and Applications
Universal Sets of n Points for One-bend Drawings of Planar Graphs with n Vertices
Discrete & Computational Geometry
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
Point-set embeddings of plane 3-trees
Computational Geometry: Theory and Applications
The hamiltonian augmentation problem and its applications to graph drawing
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Embedding plane 3-trees in R2 and R3
GD'11 Proceedings of the 19th international conference on Graph Drawing
On the hardness of point-set embeddability
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
The point-set embeddability problem for plane graphs
Proceedings of the twenty-eighth annual symposium on Computational geometry
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We give an O(nlog3n)-time linear-space algorithm that, given a plane 3-tree G with n vertices and a set S of n points in the plane, determines whether G has a point-set embedding on S (i.e., a planar straight-line drawing of G where each vertex is mapped to a distinct point of S), improving the O(n4/3+ε)-time O(n4/3)-space algorithm of Moosa and Rahman. Given an arbitrary plane graph G and a point set S, Di Giacomo and Liotta gave an algorithm to compute 2-bend point-set embeddings of G on S using O(W3) area, where W is the length of the longest edge of the bounding box of S. Their algorithm uses O(W3) area even when the input graphs are restricted to plane 3-trees. We introduce new techniques for computing 2-bend point-set embeddings of plane 3-trees that takes only O(W2) area. We also give approximation algorithms for point-set embeddings of plane 3-trees. Our results on 2-bend point-set embeddings and approximate point-set embeddings hold for partial plane 3-trees (e.g., series-parallel graphs and Halin graphs).