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Optimal algorithms to embed trees in a point set
[chapter]
1996
Lecture Notes in Computer Science
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In the degree-constrained embedding problem we are given a set of n points P where each point is assigned a positive degree and the degrees sum to 2n − 2 and are asked to embed a tree in P using straight ...
In the rootedtree embedding problem we are given a rooted tree T with n nodes and a set of n points P with one designated point p and are asked to find a straight-line embedding of T into P with the root ...
Acknowledgments We thank the referees for their suggestions on improving the presentation and organisation of this paper. ...
doi:10.1007/bfb0021791
fatcat:w42tawfy5re2dakt4vhwi3ymvi
Optimal Algorithms to Embed Trees in a Point Set
1997
Journal of Graph Algorithms and Applications
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In the degree-constrained embedding problem we are given a set of n points P where each point is assigned a positive degree and the degrees sum to 2n − 2 and are asked to embed a tree in P using straight ...
In the rootedtree embedding problem we are given a rooted tree T with n nodes and a set of n points P with one designated point p and are asked to find a straight-line embedding of T into P with the root ...
Acknowledgments We thank the referees for their suggestions on improving the presentation and organisation of this paper. ...
doi:10.7155/jgaa.00002
fatcat:4brgicth7vfktjsyadatundqju
Optimal Algorithms to Embed Trees in a Point Set
[chapter]
2002
Graph Algorithms and Applications I
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In the degree-constrained embedding problem we are given a set of n points P where each point is assigned a positive degree and the degrees sum to 2n − 2 and are asked to embed a tree in P using straight ...
In the rootedtree embedding problem we are given a rooted tree T with n nodes and a set of n points P with one designated point p and are asked to find a straight-line embedding of T into P with the root ...
Acknowledgments We thank the referees for their suggestions on improving the presentation and organisation of this paper. ...
doi:10.1142/9789812777638_0002
fatcat:7vjgypahovdwtnpk2jt7t7mzie
Planar embedding of trees on point sets without the general position assumption
2015
Turkish Journal of Mathematics
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We also give some results when the problem is limited to degree-constrained trees and point sets having constant number of collinear points. ...
The problem of point-set embedding of a planar graph G on a point set P in the plane is defined as finding a straight-line planar drawing of G such that the nodes of G are mapped one to one on the points ...
Therefore, the complexity of the problem is still open if we limit the problem to the degree-constrained trees or limit the maximum number of collinear points in the point set to a constant. ...
doi:10.3906/mat-1410-12
fatcat:kc4egztq4bb5hmotl2g6czatvy
Page 1921 of Mathematical Reviews Vol. , Issue 97C
[page]
1997
Mathematical Reviews
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In the degree- constrained embedding problem we are given a set of n points P where each point is assigned a positive degree and the degrees sum to 2m — 2 and are asked to find an embedding of a tree in ...
In the rooted-tree embedding problem we are given a rooted-tree JT with n nodes and a set of n points P with one designated point p and are asked to find a straight-line embedding of T into P with the ...
Computing Steiner points for gradient-constrained minimum networks
2010
Discrete Optimization
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A degree-3 Steiner point is labelled minimal if the total length of the three adjacent edges is minimized for a given labelling. ...
Let T g be a gradient-constrained minimum network, that is, a minimum length network spanning a given point set in 3-dimensional space with edges that are constrained to have gradients no more than an ...
The Steiner points in LMGCNs can be classified into different types, called labellings, according to whether the gradients of their incident edges are less than, equal to or greater than m when embedded ...
doi:10.1016/j.disopt.2009.10.001
fatcat:lydvisnoyrg6dngfkya7wasz4q
Semi-bipartite Graph Visualization for Gene Ontology Networks
[chapter]
2010
Lecture Notes in Computer Science
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In this paper we present algorithms which test in polynomial time if a given hypergraph H has a planar support that is (i) a path, (ii) a cycle, (iii) a tree, or (iv) a tree where the maximal degree of ...
We also show that the planar slope number of every planar partial 3-tree and also every plane partial 3-tree is at most 2 O(∆) . In particular, we answer the question of Dujmović et al. ...
doi:10.1007/978-3-642-11805-0_24
fatcat:724qxxufdzgthfzrovmnj4nzky
Overlay addressing and routing system based on hyperbolic geometry
2011
2011 IEEE Symposium on Computers and Communications (ISCC)
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Local knowledge routing schemes based on virtual coordinates taken from the hyperbolic plane have attracted considerable interest in recent years. ...
In this paper, we propose a new approach for seizing the power of the hyperbolic geometry. ...
This particular tiling splits the hyperbolic plane in distinct spaces and constructs our embedded tree. ...
doi:10.1109/iscc.2011.5983793
dblp:conf/iscc/CassagnesTBM11
fatcat:rxmfwtup7bd7bm66ipxanjtreu
Point-set embeddings of plane 3-trees
2012
Computational geometry
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We prove an Ω(n log n) lower bound on the time complexity for finding a 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. ...
Acknowledgements This work is done in Graph Drawing & Information Visualization Laboratory of the Department of CSE, BUET established under the project "Facility Upgradation for Sustainable Research on ...
doi:10.1016/j.comgeo.2011.09.002
fatcat:u5tgclkngneqfbzil5aiy3iata
Polynomial area bounds for MST embeddings of trees
2011
Computational geometry
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In their seminal paper on geometric minimum spanning trees, Monma and Suri (1992) [31] showed how to embed any tree of maximum degree 5 as a minimum spanning tree in the Euclidean plane. ...
In this paper, we show how to construct MST embeddings of arbitrary trees of maximum degree 3 and 4 within polynomial area. ...
The initial results on complete binary trees were achieved together with Roberto Tamassia. A preliminary and short version of this paper appeared in [21] . ...
doi:10.1016/j.comgeo.2011.05.005
fatcat:swszsvtmbbf47a5adxgk6m5foy
Point-Set Embeddings of Plane 3-Trees
[chapter]
2011
Lecture Notes in Computer Science
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We prove an Ω(n log n) lower bound on the time complexity for finding a 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. ...
Acknowledgements This work is done in Graph Drawing & Information Visualization Laboratory of the Department of CSE, BUET established under the project "Facility Upgradation for Sustainable Research on ...
doi:10.1007/978-3-642-18469-7_29
fatcat:4au3pwcbszawzm35espqszfiiy
A New Perspective on Clustered Planarity as a Combinatorial Embedding Problem
[article]
2015
arXiv
pre-print
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We introduce the cd-tree data structure and give a new characterization of c-planarity. It leads to efficient algorithms for c-planarity testing in the following cases. ...
Moreover, the cd-tree reveals interesting connections between c-planarity and planarity with constraints on the order of edges around vertices. ...
Conclusion In this paper we have introduced the cd-tree and we have shown that it can be used to reformulate the classic c-planarity problem as a constrained embedding problem. ...
arXiv:1506.05673v1
fatcat:pemapktu45a6hj3u4k44dhnfpa
Point-Set Embedding of Trees with Edge Constraints
[chapter]
2008
Lecture Notes in Computer Science
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Given a graph G with n vertices and a set S of n points in the plane, a point-set embedding of G on S is a planar drawing such that each vertex of G is mapped to a distinct point of S. ...
We concentrate on trees and show how to compute the output in O(n 2 log n) time and with at most 1 + 2 k/2 bends per edge, where k is the number of vertices of the given subdrawing. ...
Introduction Let G be a planar graph with n vertices and let S be a set of n points in the plane. ...
doi:10.1007/978-3-540-77537-9_14
fatcat:s7xjcoxusvgxxhkvczcvllmsoy
Fast geometric approximation techniques and geometric embedding problems
1992
Theoretical Computer Science
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We give the example of approximating the convex hull of a set of points in the plane . ..' pn > of II points in R", and an undirected graph G = (V, E) on n vertices. ...
We give fast approximation algorithms for embedding these graphs on the line and in the plane in several metrics. ...
Trees Our EMST approximation algorithm yields an approximation algorithm for embedding bounded-degree trees, such as a complete binary tree, onto points P in the plane. ...
doi:10.1016/0304-3975(92)90252-b
fatcat:wtb6nhryhrb7vptjokdrm3n4hm
Optimal Orthogonal Drawings of Planar 3-Graphs in Linear Time
[article]
2019
arXiv
pre-print
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., a planar graph with vertex degree at most three), what is the best computational upper bound to compute a bend-minimum planar orthogonal drawing of G in the variable embedding setting? ...
In this setting the algorithm can choose among the exponentially many planar embeddings of G the one that leads to an orthogonal drawing with the minimum number of bends. ...
SPQR-Trees. Let G be a biconnected graph. An SPQR-tree T of G represents the decomposition of G into its triconnected components and can be computed in linear time [8, 17, 19] . ...
arXiv:1910.11782v1
fatcat:bsfhm3dcsnbo7p4wu7vkhvj3j4
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