Computational geometry: an introduction
Computational geometry: an introduction
Introduction to algorithms
Transitions in geometric minimum spanning trees (extended abstract)
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
The realization problem for Euclidean minimum spanning trees is NP-hard
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Algorithms for drawing graphs: an annotated bibliography
Computational Geometry: Theory and Applications
Optimal Algorithms to Embed Trees in a Point Set
GD '95 Proceedings of the Symposium on Graph Drawing
Optimal-Area Upward Drawings of AVL Trees
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Proximity Constraints and Representable Trees
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Straight Line Embeddings of Planar Graphs on Point Sets
Proceedings of the 8th Canadian Conference on Computational Geometry
Graph Theory With Applications
Graph Theory With Applications
Curve-constrained drawings of planar graphs
Computational Geometry: Theory and Applications
On simultaneous planar graph embeddings
Computational Geometry: Theory and Applications
Simultaneous graph embedding with bends and circular arcs
Computational Geometry: Theory and Applications
Upward Straight-Line Embeddings of Directed Graphs into Point Sets
Graph-Theoretic Concepts in Computer Science
Constrained Point-Set Embeddability of Planar Graphs
Graph Drawing
Point-set embeddings of trees with given partial drawings
Computational Geometry: Theory and Applications
On triconnected and cubic plane graphs on given point sets
Computational Geometry: Theory and Applications
Upward straight-line embeddings of directed graphs into point sets
Computational Geometry: Theory and Applications
Plane Graphs with Parity Constraints
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Simultaneous graph embedding with bends and circular arcs
GD'06 Proceedings of the 14th international conference on Graph drawing
k-colored point-set embeddability of outerplanar graphs
GD'06 Proceedings of the 14th international conference on Graph drawing
Computing upward topological book embeddings of upward planar digraphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Point-set embedding of trees with edge constraints
GD'07 Proceedings of the 15th international conference on Graph drawing
Planar straight-line point-set embedding of trees with partial embeddings
Information Processing Letters
Upward point-set embeddability
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Upward geometric graph embeddings into point sets
GD'10 Proceedings of the 18th international conference on Graph drawing
On graphs supported by line sets
GD'10 Proceedings of the 18th international conference on Graph drawing
Point-set embeddings of plane 3-trees
GD'10 Proceedings of the 18th international conference on Graph drawing
A center transversal theorem for hyperplanes and applications to graph drawing
Proceedings of the twenty-seventh annual symposium on 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
Embedding plane 3-trees in R2 and R3
GD'11 Proceedings of the 19th international conference on Graph Drawing
Orthogeodesic point-set embedding of trees
GD'11 Proceedings of the 19th international conference on Graph Drawing
On point-sets that support planar graphs
GD'11 Proceedings of the 19th international conference on Graph Drawing
Small point sets for simply-nested planar graphs
GD'11 Proceedings of the 19th international conference on Graph Drawing
Upward point set embeddability for convex point sets is in P
GD'11 Proceedings of the 19th international conference on Graph Drawing
Universal line-sets for drawing planar 3-trees
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
On the hardness of point-set embeddability
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Capacitated domination: constant factor approximations for planar graphs
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
The point-set embeddability problem for plane graphs
Proceedings of the twenty-eighth annual symposium on Computational geometry
On point-sets that support planar graphs
Computational Geometry: Theory and Applications
Colored simultaneous geometric embeddings
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Drawing colored graphs on colored points
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Kinetic and stationary point-set embeddability for plane graphs
GD'12 Proceedings of the 20th international conference on Graph Drawing
Point-Set embeddability of 2-colored trees
GD'12 Proceedings of the 20th international conference on Graph Drawing
On upward point set embeddability
Computational Geometry: Theory and Applications
Plane 3-trees: embeddability and approximation
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Universal point sets for planar three-trees
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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Given an n-vertex outer-planar graph G and a set P of n points in the plane, we present an O(n log3 n) time and O(n) space algorithm to compute a straight-line embedding of G in P, improving upon the algorithm in [8,12] that requires O(n2) time. Our algorithm is near-optimal as there is an ω (n log n) lower bound for the problem [4]. We present a simpler O(nd) time and O(n) space algorithm to compute a straight-line embedding of G in P where log n ≥ d ≥ 2n is the length of the longest vertex disjoint path in the dual of G. Therefore, the time complexity of the simpler algorithm varies between O(n log n) and O(n2) depending on the value of d. More efficient algorithms are presented for certain restricted cases. If the dual of G is a path, then an optimal Θ (n log n) time algorithm is presented. If the given point set is in convex position then we show that O(n) time suffices.