A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Point-set embeddings of plane 3-trees

2012
*
Computational geometry
*

We prove an Ω(n log n) lower bound on the time complexity for finding a

doi:10.1016/j.comgeo.2011.09.002
fatcat:u5tgclkngneqfbzil5aiy3iata
*point*-*set**embedding**of*a*plane**3*-*tree*. ... In this paper, we give an O (n 2 ) 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. ... Graph Drawing & Information Visualization" supported by the Ministry*of*Science and Information & Communication Technology, Government*of*Bangladesh. ...##
###
Point-Set Embeddings of Plane 3-Trees
[chapter]

2011
*
Lecture Notes in Computer Science
*

We prove an Ω(n log n) lower bound on the time complexity for finding a

doi:10.1007/978-3-642-18469-7_29
fatcat:4au3pwcbszawzm35espqszfiiy
*point*-*set**embedding**of*a*plane**3*-*tree*. ... In this paper, we give an O (n 2 ) 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. ... Graph Drawing & Information Visualization" supported by the Ministry*of*Science and Information & Communication Technology, Government*of*Bangladesh. ...##
###
On the Hardness of Point-Set Embeddability
[chapter]

2012
*
Lecture Notes in Computer Science
*

*plane*

*3*-

*trees*. ... A

*point*-

*set*

*embedding*

*of*a

*plane*graph G with n vertices on a

*set*S

*of*n

*points*is a straight-line drawing

*of*G, where the vertices

*of*G are mapped to distinct

*points*

*of*S. ... 2-connected

*plane*graph admits a

*point*-

*set*

*embedding*on a given

*set*

*of*

*points*[5] . ...

##
###
Embedding Plane 3-Trees in ℝ2 and ℝ3
[chapter]

2012
*
Lecture Notes in Computer Science
*

In this paper, we give an O(n 4/

doi:10.1007/978-3-642-25878-7_5
fatcat:kqhbp346njdkvhpuapjhq7otsu
*3*+ )expected time algorithm to decide whether a*plane**3*-*tree*with n vertices admits a*point*-*set**embedding*on a given*set**of*n*points*in general position in R 2 and compute ... We also prove that given a*plane**3*-*tree*G with n vertices, a*set*P*of*n*points*in R*3*that are not necessarily in general position and a mapping*of*the three outer vertices*of*G to three different*points*...*Point*-*Set**Embeddings**of**Plane**3*-*Trees*in R*3*Given a*plane**3*-*tree*G with n vertices, a*set*P*of*n*points*(not necessarily in general position) in R 2 and a mapping for the outer vertices*of*G to three ...##
###
Improved Algorithms for the Point-Set Embeddability problem for Plane 3-Trees
[article]

2010
*
arXiv
*
pre-print

In the

arXiv:1012.0230v1
fatcat:s3nj7txthrbypfepwidhum3nam
*point**set*embeddability problem, we are given a*plane*graph G with n vertices and a*point**set*S with n*points*. ... Recently, in DBLP:conf/gd/NishatMR10, a complete characterization for this problem on a special class*of*graphs known as the*plane**3*-*trees*was presented along with an efficient algorithm to solve the problem ... A*plane**3*-*tree**of*17 vertices Fig. 2 . 2 The representative*tree**of*the*plane**3*-*tree**of*Fig.*3*.*3*An example*of**point**set**embedding**of*a*plane**3*-tree.Example 1 InFigure*3*(a) we present an example ...##
###
Complexity of Planar Embeddability of Trees inside Simple Polygons
[article]

2009
*
arXiv
*
pre-print

Geometric

arXiv:0908.4041v1
fatcat:yzotlcqzuzcjvoroiktsi3q52e
*embedding**of*graphs in a*point**set*in the*plane*is a well known problem. ... Given a*point**set*in the*plane*bounded by a simple polygon and a free*tree*, we show that deciding whether there is a planar straight-line*embedding**of*the*tree*on the*point**set*inside the simple polygon ... Let P be a*set**of*n*points*in the*plane*inside a simple polygon S, and let T be a n-node free*tree*. ...##
###
On Universal Point Sets for Planar Graphs
[article]

2013
*
arXiv
*
pre-print

A

arXiv:1209.3594v5
fatcat:qyfi76fkuvcclkcg4eo63e5aje
*set*P*of**points*in R^2 is n-universal, if every planar graph on n vertices admits a*plane*straight-line*embedding*on P. ... Finally, we describe a collection G*of*7'393 planar graphs on 35 vertices that do not admit a simultaneous geometric*embedding*without mapping, that is, no*set**of*35*points*in the*plane*supports a*plane*... Hence not every planar*3*-*tree*on 15 vertices can be*embedded*on any given*set**of*15*points*. ...##
###
On Universal Point Sets for Planar Graphs
[chapter]

2013
*
Lecture Notes in Computer Science
*

A

doi:10.1007/978-3-642-45281-9_3
fatcat:aw5pswv7ejcobhaphx7ldetrxa
*set*P*of**points*in R 2 is n-universal if every planar graph on n vertices admits a*plane*straight-line*embedding*on P . ... Finally, we describe a collection G*of*7 393 planar graphs on 35 vertices that do not admit a simultaneous geometric*embedding*without mapping, that is, no*set**of*35*points*in the*plane*supports a*plane*... Proof: Let P ⊂ R 2 be a*set**of*n*points*and denote by F n ⊆ T n the*set**of*labeled planar*3*-*trees*from T n that admit a*plane*straight-line*embedding*onto P . ...##
###
On Universal Point Sets for Planar Graphs

2015
*
Journal of Graph Algorithms and Applications
*

A

doi:10.7155/jgaa.00374
fatcat:ehvzq7d4ezb3dpzpik7a6rbk4y
*set*P*of**points*in R 2 is n-universal if every planar graph on n vertices admits a*plane*straight-line*embedding*on P . ... Finally, we describe a collection G*of*7 393 planar graphs on 35 vertices that do not admit a simultaneous geometric*embedding*without mapping, that is, no*set**of*35*points*in the*plane*supports a*plane*... Proof: Let P ⊂ R 2 be a*set**of*n*points*and denote by F n ⊆ T n the*set**of*labeled planar*3*-*trees*from T n that admit a*plane*straight-line*embedding*onto P . ...##
###
Straight-Line Embeddings of Two Rooted Trees in the Plane

1999
*
Discrete & Computational Geometry
*

We prove the following theorem: Let T 1 and T 2 be two disjoint rooted

doi:10.1007/pl00009441
fatcat:rqsirivg2nclhol4wjdux2ggcq
*trees*with roots v 1 and v 2 , respectively, and let P be a*set**of*|T 1 ∪ T 2 |*points*in the*plane*in general position containing ... Moreover, we give a O(n 2 log n) time algorithm for finding such an*embedding*, where n is the number*of*vertices contained in T 1 ∪ T 2 . ... Acknowledgments The authors would like to thank Hitoshi Suzuki for his helpful suggestions on the complexities*of*algorithms. They would also like to thank the referees for their helpful comments. ...##
###
On embedding an outer-planar graph in a point set
[chapter]

1997
*
Lecture Notes in Computer Science
*

Given an n-vertex outer-planar graph G and a

doi:10.1007/3-540-63938-1_47
fatcat:ojzi4kaw4fetpawt72coecrqd4
*set*P*of*n*points*in the*plane*, we present an O(nlog s n) time and O(n) space algorithm to compute a straight-line*embedding**of*G in P, improving upon the algorithm ... If the dual*of*G is a path, then an optimal O(n log n) time algorithm is presented. If the given*point**set*is in convex position then we show that O(n) time suffices. ... Acknowledgements: The author wishes to thank Kilani Ghoudi for helpful discussions on this topic, and Janos Pach for*pointing*out some missing references. ...##
###
Universal Line-Sets for Drawing Planar 3-Trees
[chapter]

2012
*
Lecture Notes in Computer Science
*

In this paper we show that a

doi:10.1007/978-3-642-28076-4_15
fatcat:oeaxafsnqbfnhlphusp5pijtlm
*set**of*n−*3*2 +*3*parallel lines or a*set**of*n+*3*4 concentric circles are universal for drawing planar*3*-*trees*with n vertices. ... A by-product*of*our algorithm is the generalization*of*the known bijection between*plane**3*-*trees*and rooted full ternary*trees*to the bijection between planar*3*-*trees*and unrooted full ternary*trees*. ... Acknowledgment We thank the Ministry*of*Science and Information & Communication Technology, Government*of*Bangladesh for supporting the project "Facility Upgradation for Sustainable Research on Graph Drawing ...##
###
Universal Line-Sets for Drawing Planar 3-Trees

2013
*
Journal of Graph Algorithms and Applications
*

In this paper we show that a

doi:10.7155/jgaa.00285
fatcat:nucchstwcjd3nb4zgmcy4kli6e
*set**of*n−*3*2 +*3*parallel lines or a*set**of*n+*3*4 concentric circles are universal for drawing planar*3*-*trees*with n vertices. ... A by-product*of*our algorithm is the generalization*of*the known bijection between*plane**3*-*trees*and rooted full ternary*trees*to the bijection between planar*3*-*trees*and unrooted full ternary*trees*. ... Acknowledgment We thank the Ministry*of*Science and Information & Communication Technology, Government*of*Bangladesh for supporting the project "Facility Upgradation for Sustainable Research on Graph Drawing ...##
###
The Connectivities of Leaf Graphs of Sets of Points in the Plane

2001
*
Tokyo Journal of Mathematics
*

Let U be a

doi:10.3836/tjm/1255958194
fatcat:fwgv6okcfrgkvjlg754elvxftm
*set**of*n*points*in the*plane*. If no three*points*are collinear, then we s a y ... Glicia, A note on the*tree*g r aph*of*a*set**of**points*in the*plane*, Proc.*of*9th Canadian conference on comput. geom., (1997), 46-49 [*3*] Y. Ikebe, M. Perles, A. Tamura and S. ... [*3*] showed that any rooted*tree*with n vertices can be*embedded*as a non-selntersecting*tree*on a given*set*U, the root being mapped to an arbitrary specied*point**of*U. Furthermore A. ...##
###
Approximating minimum Steiner point trees in Minkowski planes

2010
*
Networks
*

Given a

doi:10.1002/net.20376
fatcat:f3wpqkvkojhexh75kr3h6w5hbu
*set**of**points*, we define a minimum Steiner*point**tree*to be a*tree*interconnecting these*points*and possibly some additional*points*such that the length*of*every edge is at most 1 and the number ... We also introduce a new canonical form for minimum Steiner*point**trees*in the Euclidean*plane*; this demonstrates that minimum Steiner*point**trees*are shortest total length*trees*with a certain discrete-edge-length ... The authors wish to thank Jamie Evans for partaking in many fruitful discussions during the development*of*this paper. We would also like to thank the referees for their insightful comments. ...
« Previous

*Showing results 1 — 15 out of 85,533 results*