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Point-Set Embedding of Trees with Edge Constraints
[chapter]

2008
*
Lecture Notes in Computer Science
*

A geometric

doi:10.1007/978-3-540-77537-9_14
fatcat:s7xjcoxusvgxxhkvczcvllmsoy
*point*-*set**embedding*is a*point*-*set**embedding**with*no*edge*bends. ... 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. ... Conclusions and Open Problems This paper introduced the problem*of*computing a*point*-*set**embedding**of*a graph G on a*set*S*of**points*,*with*the*constraint*that a partial straight-line planar drawing*of*...##
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Treedecomposition of geometric constraint graphs based on computing graph circuits

2009
*
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling on - SPM '09
*

First the geometric problem is translated into a graph whose vertices represent the

doi:10.1145/1629255.1629270
dblp:conf/sma/Joan-ArinyoTV09
fatcat:iz6ic5m67nbfliora4ad4jb55q
*set**of*geometric elements and whose*edges*are the*constraints*. ... The algorithm recursively first computes a*set**of*fundamental circuits in the graph then splits the graph into a*set**of*subgraphs each sharing exactly three vertices*with*the fundamental circuit. ... We consider 2D geometric*constraint*problems defined by a*set**of*geometric elements like*points*, lines, line segments, circles and circular arcs*with*fixed radius, along*with*a*set**of**constraints*like ...##
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Page 5896 of Mathematical Reviews Vol. , Issue 98I
[page]

1998
*
Mathematical Reviews
*

In the rooted-

*tree**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 ... 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 embed a*tree*in P using straight ...##
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Optimizing over All Combinatorial Embeddings of a Planar Graph (Extended Abstract)
[chapter]

1999
*
Lecture Notes in Computer Science
*

Our computational results on two benchmark

doi:10.1007/3-540-48777-8_27
fatcat:o3wxj5r625h7tkcmqj3ufqoipu
*sets**of*graphs are surprising: The number*of*variables and*constraints*seems to grow only linearly*with*the size*of*the graphs although the number*of**embeddings*... We characterize the*set**of*all possible*embeddings**of*a given biconnected planar graph G by means*of*a system*of*linear inequalities*with*f0; 1gvariables corresponding to the*set**of*those cycles in G which ... Di Battista in Rome for giving us the opportunity to use their implementation*of*SPQR-*trees*in GDToolkit, a software library that is part*of*the ESPRIT ALCOM-IT project (work package 1.2), and to use their ...##
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A New Perspective on Clustered Planarity as a Combinatorial Embedding Problem
[article]

2015
*
arXiv
*
pre-print

Moreover, the cd-

arXiv:1506.05673v1
fatcat:pemapktu45a6hj3u4k44dhnfpa
*tree*reveals interesting connections between c-planarity and planarity*with**constraints*on the order*of**edges*around vertices. ... (i) Every cluster and every co-cluster (complement*of*a cluster) has at most two connected components. (ii) Every cluster has at most five outgoing*edges*. ... We believe that the constrained*embedding*problems we defined provide a promising starting*point*for further research, e.g., by studying restricted variants to further deepen the understanding*of*the c-planarity ...##
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A New Perspective on Clustered Planarity as a Combinatorial Embedding Problem
[chapter]

2014
*
Lecture Notes in Computer Science
*

(ii) Every cluster has at most five outgoing

doi:10.1007/978-3-662-45803-7_37
fatcat:e5u22xwsn5h5bf6pixz4425zlm
*edges*. Moreover, the cd-*tree*reveals interesting connections between c-planarity and planarity*with**constraints*on the order*of**edges*around vertices. ... We first present the cd-*tree*data structure (Sec. 3) and use it to characterize c-planarity in terms*of*combinatorial*embeddings**of*planar graphs. ... A family*of*order-*constraints*for the*set*S is a*set**of*different order*constraints*, i.e., a subset*of*the power*set**of*O S . ...##
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Bend Minimization in Planar Orthogonal Drawings Using Integer Programming

2006
*
SIAM Journal on Optimization
*

Our approach for biconnected graphs combines an integer linear programming (ILP) formulation for the

doi:10.1137/040614086
fatcat:q2giaw2mw5gktixad3tczybv7y
*set**of*all*embeddings**of*a planar graph*with*the network flow formulation for fixed*embeddings*. ... While the problem can be solved via network flow for a given planar*embedding**of*a graph G, it is NP-hard if we consider the*set**of*all planar*embeddings**of*G. ... Acknowledgment We thank Walter Didimo for providing the code*of*the branch & bound algorithm and the real world benchmark*set*. ...##
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Crossing Minimization and Layouts of Directed Hypergraphs with Port Constraints
[chapter]

2011
*
Lecture Notes in Computer Science
*

Most existing algorithms for drawing hypergraphs

doi:10.1007/978-3-642-18469-7_13
fatcat:2efprs4nvrhojfoy4gdnt5uwsi
*with*port*constraints*are adaptions*of*the framework originally proposed by Sugiyama et al. in 1981 for simple directed graphs. ... Many practical applications for drawing graphs are modeled by directed graphs*with*domain specific*constraints*. ... A generic approach to model this*set**of*orders for each node is by using*embedding**constraints*, which define a*tree*structure*of**constraint*nodes [12] . ...##
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Simultaneous Embedding of Planar Graphs with Few Bends
[chapter]

2005
*
Lecture Notes in Computer Science
*

We also describe an O(n) time algorithm for simultaneous

doi:10.1007/978-3-540-31843-9_21
fatcat:335gpmzsijalddsrbxfbfw426u
*embedding**with*fixed-*edges*for*tree*-path pairs on the O(n) × O(n 2 ) grid*with*at most one bend per*tree*-*edge*and no bends along path*edges*. ... We present an O(n) time algorithm for simultaneous*embedding**of*pairs*of*planar graphs on the O(n 2 )×O(n 2 ) grid,*with*at most three bends per*edge*, where n is the number*of*vertices. ... Acknowledgments We would like to thank Michael Kaufmann and David Eppstein for the interesting discussions about the problems discussed in the paper, and Petr Moravsky for helping*with*the implementation ...##
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Directional Routing via Generalized st-Numberings

2000
*
SIAM Journal on Discrete Mathematics
*

We also show that a directed acyclic graph (dag) that is k-connected to a

doi:10.1137/s0895480198333290
fatcat:kbuoqwaxwzffjn3yukzf3luvzy
*set**of*sinks has a k-directional*embedding*in (k − 1)-space*with*the sink*set*as the extreme nodes. ... We prove that all 3-connected graphs have 3-directional*embeddings*in the plane so that each node outside a*set**of*extreme nodes has a neighbor in each*of*the three directional regions defined in the plane ... We now show that it is still possible to "split" a*set**of*three*points*in the plane into three directions even*with*the addition*of*many new directional*constraints**of*a certain type. Proof. ...##
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Testing Simultaneous Planarity when the Common Graph is 2-Connected
[article]

2011
*
arXiv
*
pre-print

Our algorithm extends to the case

arXiv:1009.4517v2
fatcat:w2byi7riszdphdpiiazgszsu6u
*of*k planar graphs where each vertex [*edge*] is either common to all graphs or belongs to exactly one*of*them. ... Two planar graphs G1 and G2 sharing some vertices and*edges*are 'simultaneously planar' if they have planar drawings such that a shared vertex [*edge*] is represented by the same*point*[curve] in both drawings ... At any*point*we will have two*sets**of*PQ-*trees*representing the partial planar*embeddings**of*the subgraphs*of*G 1 and G 2 induced by the vertices added so far. ...##
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Algorithms for Metric Learning via Contrastive Embeddings

2019
*
International Symposium on Computational Geometry
*

Given a universe X and

doi:10.4230/lipics.socg.2019.45
dblp:conf/compgeom/IharaMS19
fatcat:2g55vn33yjdmrf34x7rjv6syua
*sets*S, D ⊂ X 2*of*similar and dissimilar pairs, we seek to find a mapping f : X → Y , into some target metric space M = (Y, ρ), such that similar objects are mapped to*points*at ... We study the problem*of*supervised learning a metric space under discriminative*constraints*. ... Let G S be the graph*with*vertex*set*V (G S ) = X, and*edge**set*E(G S ) = S. We use ρ S to denote the shortest-path distance*of*G S , where the length*of*each*edge*is*set*to u. Lemma 10. ...##
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Testing Simultaneous Planarity When the Common Graph Is 2-Connected
[chapter]

2010
*
Lecture Notes in Computer Science
*

Two planar graphs G1 and G2 sharing some vertices and

doi:10.1007/978-3-642-17514-5_35
fatcat:2oyhp5srm5fo3dc4erwajhs2zq
*edges*are simultaneously planar if they have planar drawings such that a shared vertex [*edge*] is represented by the same*point*[curve] in both drawings ... Our algorithm extends to the case*of*k planar graphs where each vertex [*edge*] is either common to all graphs or belongs to exactly one*of*them, and the common subgraph is 2-connected. ... In particular we want to thank one referee for help*with*the drawing method in Section 4.3. ...##
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Graph Embedding with Topological Cycle-Constraints
[chapter]

1999
*
Lecture Notes in Computer Science
*

We address the problem

doi:10.1007/3-540-46648-7_16
fatcat:eji2fxjs35g5vmtpghb7adnkqy
*of*nding a planar*embedding**of*a graph satisfying a*set**of**constraints*between its vertices and cycles that require*embedding*a given vertex inside its corresponding cycle. ... This paper concerns graph*embedding*under topological*constraints*. ... Thus, we are concerned*with*the problem*of*nding a planar*embedding**of*a graph satisfying a given*set**of*cycle-*constraints*. ...##
###
Simultaneous Embedding of Planar Graphs with Few Bends

2005
*
Journal of Graph Algorithms and Applications
*

We also describe an O(n) time algorithm for simultaneous

doi:10.7155/jgaa.00113
fatcat:jnloyknqozbxzkf4a6wlmxeadq
*embedding**with*fixed-*edges*for*tree*-path pairs on the O(n) × O(n 2 ) grid*with*at most one bend per*tree*-*edge*and no bends along path*edges*. ... We present an O(n) time algorithm for simultaneous*embedding**of*pairs*of*planar graphs on the O(n 2 )×O(n 2 ) grid,*with*at most three bends per*edge*, where n is the number*of*vertices. ... Acknowledgments We would like to thank Michael Kaufmann and David Eppstein for the interesting discussions about the problems discussed in the paper, and Petr Moravsky for helping*with*the implementation ...
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