Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On embedding an outer-planar graph in a point set
Computational Geometry: Theory and Applications
Drawing planar 3-trees with given face-areas
GD'09 Proceedings of the 17th 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
Point-set embeddings of plane 3-trees
Computational Geometry: Theory and Applications
Embedding plane 3-trees in R2 and R3
GD'11 Proceedings of the 19th international conference on Graph Drawing
Drawing planar 3-trees with given face areas
Computational Geometry: Theory and Applications
Hi-index | 0.00 |
A straight-line drawing of a plane graph G is a planar drawing of G, where each vertex is drawn as a point and each edge is drawn as a straight-line segment. Given a set S of n points on the Euclidean plane, a point-set embedding of a plane graph G with n vertices on S is a straight-line drawing of G, where each vertex of G is mapped to a distinct point of S. The problem of deciding if G admits a point-set embedding on S is NP-complete in general and even when G is 2-connected and 2-outerplanar. In this paper we give an O(n2 log n) time algorithm to decide whether a plane 3-tree admits a point-set embedding on a given set of points or not, and find an embedding if it exists. We prove an Ω(n log n) lower bound on the time complexity for finding a point-set embedding of a plane 3-tree. Moreover, we consider a variant of the problem where we are given a plane 3-tree G with n vertices and a set S of k n points, and give a polynomial time algorithm to find a point-set embedding of G on S if it exists.