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Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up1
Tamara Mchedlidze
Algorithms for Graph Visualization
INSTITUT FUR THEORETISCHE INFORMATIK · FAKULTAT FUR INFORMATIK
Wrap Up
6.2.2017
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up2
Organizational
Oral Exam (20 Minutes)13,14 February 201720,21 March 2017Room 315Myself + Benjamin (or substitute) taking protocall.Language: English.
Exams
ContentMaterial from lectures/exercisesSkript, Slides, Blackboard proofs - only what have beendiscussed
GoalsLayout problems (Problem definitions, Aesthetic criteria)Algorithms (Proof ideas)
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up3
Layout Problem – General Definition
given: Graph G = (V,E)find: (good) drawing Γ of G, that
complies with drawing conventionsoptimizes aestheticssatisfies local/partial constraints
Graph visualization problem
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up4
Material Overview
Graph ClassesDrawing Conventions, Aesthetic CriteriaAlgorithms and their type (D & C, Incremental,LP)Techniques
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up4
Material Overview
Graph ClassesDrawing Conventions, Aesthetic CriteriaAlgorithms and their type (D & C, Incremental,LP)Techniques
Let’s Draw a Graph!
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up5
Topic 1: Trees
Layered LayoutAesthetics: symmetry, areaConventions: planarity, vert. on layersAlgorithm: Divide&Conquer, TimeO(n), Area O(n2)
HV-LayoutAesthetics: symmetry, areaConvention: h/v edges, planarityAlgorithm: Divide&Conquer, TimeO(n), Area O(n log n)
Radial LayoutAesthetics: vertex distributionConvention: vertices on co-centric circles,planarityAlgorithm: Divide&Conquer, Time O(n)
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up6
Topic 2: Series-Parallel Graphs
Convention: planarity, upwardnessAesthetics: symmetry, vertical automorphismsAlgorithm: Divide&Conquer based on SPQ-decomposition,Time O(n), Area O(n2). Embedding varies.Area lower bound with fixed embedding Ω(4n)
PP
Gn+1
Gn
sn+1
sn
tn
tn+1
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up7
Topic 3: Planar Graphs - Shift Algorithm
Conventions: planarityAesthetics: ... ?Algorithm: Incremental based on Canonical Ordering.Time O(n), Area O(n2). Embedding fixed.Highlights: Proof of planarity, linear time implementationbased on relative x-distances
+1 +2
root
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up8
Topic 4: Planar Graphs - Schnyder Realizer
Conventions: planarityAesthetics: ... ?Algorithm: Based on Barycentric representation,Schnyder forest. Time O(n), Area O(n2). Embeddingfixed.Highlights: Proof of planarity of baricentric representation,Schnyder forest - useful tool on its own.
T1
T2
T3
T3
T2
T1
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up9
Topic 5: General Graphs - Force Directed
Conventions: ...Aesthetics: edge lengthAlgorithm: Eades, Fruchteman-Reingold. Time O(n2) periteration.Modifications: Inertia, Gravitation, Magnetic Forces.Bounded Drawing area.Adaptive displacement.Computation of forces using Quad-tree - Time O(n log n)per iteration. Multilevel approach - Time O(n log2 n) overall.
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up10
Topic 6: Directed Graphs - Layered Layout
Conventions: vertices on layers, edges upwardAesthetics: upwardness, edge length, edge bends, edgestraightness, drawing width/ height, crossings.Algorithm: Sugiyama Framework.Resolve cycles - Heuristic solutions. Time O(|V |+ |A|).Layer Assignement - minimize height: topologicalnumbering (O(|V |+ |A|)), total edge length: ILPCrossing Minimization - swap. Two layers: heuristics:barycenter, median (approximation factor) (O(|V |+ |A|)),ILP.Node Positioning - edge straightness: quadratic program.
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up11
Topic 7: Degree 4 - Orthogonal Drawings
Conventions: Edges on grid.Aesthetics: Height, Width, Bends
Algorithm: Biedl& Kant: incremental algorithm. TimeUses ear-decomposition, topological ordering. Time O(n).Area O(n2).
Highlights: Planar Drawing in case of Planar EmbeddedGraphs
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up12
Topic 8: Degree 4 - Orthogonal Drawings - Flow
Conventions: Edges on grid.Aesthetics: Height, Width, Bends
Algorithm: Topology-shape-metric.Crossing ReductionBend Minimization: Orthogonal Representation. FlowNetwork. Time O(n3/2)Area Minimization: All faces rectangles: total edgelength, area, flow network. Time O(n3/2). Topologicalnumbering. Rectlinear faces - face refinement.
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up13
Topic 9: Upward Planarity
Conventions: Planarity, Edges UpwardAesthetics: ...
Algorithm: Characterization (drawing planar st-digraphs),Assignement vertices to faces, Flow Network, Facesubdivition. Time O(n2).
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up14
Topic 10: Contact Representations
Conventions: Vertices polygons, Edges-contactsAesthetics: Complexity of polygons
Algorithm: Rectangular dual. Characterization. RegularEdge Labeling, Canonical Ordering, st-digraphs, topologicalordering. Time O(n).
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up15
Visualization of GD Publications
Graph Drawing Contest holding at Graph Drawingconference each September
This year graph: data of all publications in the Proceedingsof Graph Drawing between 1994 and 2015
id, title, authors,institution,cites, citedby, year
task: nice visualization
it is not compulsory to make use of the extra data
1 Submission: by Sophie von Schmettow
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up15
Visualization of GD Publications
Graph Drawing Contest holding at Graph Drawingconference each September
This year graph: data of all publications in the Proceedingsof Graph Drawing between 1994 and 2015
id, title, authors,institution,cites, citedby, year
task: nice visualization
it is not compulsory to make use of the extra data
1 Submission: by Sophie von Schmettow
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up15
Visualization of GD Publications
Graph Drawing Contest holding at Graph Drawingconference each September
This year graph: data of all publications in the Proceedingsof Graph Drawing between 1994 and 2015
id, title, authors,institution,cites, citedby, year
task: nice visualization
it is not compulsory to make use of the extra data
1 Submission: by Sophie von Schmettow
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up15
Visualization of GD Publications
Graph Drawing Contest holding at Graph Drawingconference each September
This year graph: data of all publications in the Proceedingsof Graph Drawing between 1994 and 2015
id, title, authors,institution,cites, citedby, year
task: nice visualization
it is not compulsory to make use of the extra data
1 Submission: by Sophie von Schmettow
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up15
Visualization of GD Publications
Graph Drawing Contest holding at Graph Drawingconference each September
This year graph: data of all publications in the Proceedingsof Graph Drawing between 1994 and 2015
id, title, authors,institution,cites, citedby, year
task: nice visualization
it is not compulsory to make use of the extra data
1 Submission: by Sophie von Schmettow
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up16
Visualization of GD Publications
Sophie von Schmettow
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up17
Practical Course on Graph Visualization
Background: International Symposium on Graph Drawing (GD)and Graph Drawing Challenge
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up17
Practical Course on Graph Visualization
Background: International Symposium on Graph Drawing (GD)and Graph Drawing Challenge
Task: develop software for a givengraph visualization problem
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up17
Practical Course on Graph Visualization
Background: International Symposium on Graph Drawing (GD)and Graph Drawing Challenge
Task: develop software for a givengraph visualization problem
2014Area Minimization for Orthogonal Drawingspart of the lecturebest team won graph drawing contest
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up17
Practical Course on Graph Visualization
Background: International Symposium on Graph Drawing (GD)and Graph Drawing Challenge
Task: develop software for a givengraph visualization problem
2014Area Minimization for Orthogonal Drawingspart of the lecturebest team won graph drawing contest
2015Crossing Minimization in Book Embeddingsseparate courseone team - collaborative worksecond place at the contestBest Poster Award in 2016
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up17
Practical Course on Graph Visualization
Background: International Symposium on Graph Drawing (GD)and Graph Drawing Challenge
Task: develop software for a givengraph visualization problem
2017Maximizing the AnglesBetween Crossing Edges in Straight-line Drawings5 credit points8 participants (registration by email to me)
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up18
HiWi Place
Visualization of Citation Network of Graph DrawingPublications
Target: participate in the GD contestTrying out various layout styles (edge bundling),clustering methodsImplementation (D3 or other framework)Clustering MethodsTopic Extraction and Labeling Methods
Topic
DetailsUp to 40 hours/monthSend your requests to me
Dr. Tamara Mchedlidze · Algorithms for Graph Visualization Wrap up19
HiWi Place (Master’s Thesis possible)
Visualization of Text Variant Graphs and Sonic Topilogy ofPoems with Curves
Topics
DetailsUp to 40 hours/monthSend your requests to me
Basic Computational Geometry Problems: routing curvethrough obstacles, minimizing curve complexity.Text variant: obstacles can move, Sonic Topology:obstacles do not move
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