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1 The Future of Graph Drawing and a rhapsody Peter Eades

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2 Question: What is the future of Graph Drawing? Answer:... I’ll tell you later... But first: some constraints, and a brief history....

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3 Extrovert I do research to make some impact on the world I want to solve problems posed by others I want to make the world a better place Introvert I do research because I really want to know the answer I am driven to uncover the truth I am driven by my personal curiosity Two different motivations for research Constraint: This talk is mostly aimed at extroverts

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4 What is the relationship between extroverted research and the real world? Research that is inspired by the real world Research that is useful for the real world Note: Fundamental research (“theory”) is usually inspired by the real world extroverted research

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5 A brief history

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6 1970s An idea emerges: Visualise graphs using a computer! Inspired by the need for better human decision making Implementations aimed at business decision making, circuit schematics, software diagrams, organisation charts, network protocols, and graph theory Some key ideas defined Aesthetic criteria defined (intuitively) Key scientific challenge defined: layout to optimise aesthetic criteria

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7 1980s Exciting algorithms and geometry: Many fundamental graph layout algorithms designed, enunciated, implemented, and analysed Extra inspirational ideas from graph theory, geometry, and algorithmics Planarity becomes a central concept

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8 1990s Maturity Graph Drawing matures as a discipline The Graph Drawing Conference begins The academic Graph Drawing “community” emerges More demand High data volumes increase demand for visualization Small companies appear More communities Information Visualization discipline appears

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9 2000s Even more demand Data volumes become higher than ever imagined, and demand for visualization increases accordingly New customers: systems biology, social networks, security,... Better engineering More usable products, both free and commercial More companies started, older companies become stable Invisibility Graph drawing algorithms become invisible in vertical tool

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10 Question: What is the future of Graph Drawing? Answer:... I’ll tell you later... But first: A rhapsody: unsupported conjectures, subjective observations, outlandish claims, a few plain lies, and some open problems

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11 Subjective Observation: Graph Drawing is successful

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12 Graph Drawing is successful Algorithms for graph drawing are used in many industries: Biotechnology Software engineering Networks Business intelligence Security Graph drawing software is an industry: Employs about 500 FTE people Market worth up to $100,000,000 per year About 100 FTE researchers Graph Drawing is scientifically significant Graph Drawing has provided an elegant algorithmic approach to the centuries-old interplay between combinatorial and geometric structures GD2010 is a “rank A” conference Graph drawing papers appear in many top journals and conference proceedings

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13 “Graph Drawing is the big success story in information visualization” Stephen North, September 2010

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14 Subjective Observation: Graph Drawing is connected to many other disciplines

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15 Keith Nesbitt 2003: use metro map metaphor for abstract data connections

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16 GraphDrawing GraphicArt Algorithms HCI DataMining Computer Graphics Computational Geometry CombinatorialGeometry LinearAlgebra Info Vis GraphTheory Graph Drawing: Connections VisualLanguages Computer Science

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17 Biology Social Networks Computer Science Security GraphDrawing DataMining InfoVis HD DataVis Finance

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18 Unsolved problem: make a really good metro map of graph drawing connections Based on real data Each metro line represents a community, as instantiated by a conference Each station joining different lines indicates that there are papers co- authored by people in different communities GraphD rawing Grap hicAr t Algori thms HCIHCI Data Minin g Comp uter Graph ics Computa tional Geometr y CombinatorialG eometry LinearA lgebra Inf o Vis GraphTh eory Graph Drawing: Connection s VisualLan guages $10 +

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19 GraphD rawing Grap hicAr t Algori thms HCIHCI Data Minin g Comp uter Graph ics Computa tional Geometr y CombinatorialG eometry LinearA lgebra Inf o Vis GraphTh eory Graph Drawing: Connection s VisualLan guages Unsolved problem: Create algorithms and systems to draw (ordered) hypergraphs in the metro-map metaphor.

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20 Outlandish claim: Graph Drawing is dying

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21 Interview with a Very Experienced Industry Researcher in a Telco, Sept 14, 2010 “Scale! Those force directed algorithms run much faster now than they did around 2000, using the Koren/Quigley/Walshaw methods!” Interviewer: “What are the most useful results from the Graph Drawing researchers in the last ten years?” Industry Researcher: … … “For force directed methods, visual complexity is now a problem ….”

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22 Interview with a Very Experienced Industry Researcher in a Telco, Sept 14, 2010 Interviewer: “Any other useful results from the Graph Drawing researchers in the last ten years?” Industry Researcher: … … … … “No”

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23 Interview with the CEO and CTO of a Graph Drawing software company, Sept 15, 2010 CTO:“Yes. We implemented some of them. We had to fix them a bit, but they gave us much better runtimes.” Interviewer: “Any other useful results from the Graph Drawing researchers in the last ten years?” Industry people:.... Interviewer: “What are the most useful results from the Graph Drawing researchers in the last ten years?” CTO:“Fast force directed methods. When was that?” Interviewer: “Around GD2000, I think... Almost 10 years ago.” CEO: “I know one thing: nested drawings. This models the data better than previously.” Interviewer: “Anything else?”

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24 Interview with the CEO and CTO of a Graph Drawing software company, Sept 15, 2010 CEO: “Well, our tools are much better engineered than “ten years ago. We’ve spent a lot of energy...” Interviewer: “Yes, but I guess that kind of thing didn’t come from the Graph Drawing research community?” CEO: “Oh, I guess not.” … … CIO: “I don’t think we have used any of the other results. They are certainly interesting, but...”

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25 Data source: citeceer

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26 1980 1990 2000 2010 50% 100% Data source: none Quality of drawings 85% Unsubstantiated claim: the quality of graph drawings isn’t getting any better.

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27 Open Problem: Is it worth the money?

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28 Average cost of Graph Drawing Researcher per year (assuming $100Kpa, 2.5 oncost multiplier) = $250K. There are probably about 100 FTE GD researchers in the world. The cost of the past ten years of Graph Drawing Research is about $25M Open Problem: Has the world made a profit from this $25M investment yet? If not, how long will it take to get some ROI? $250M

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29 85% 1980 1990 2000 2010 100% Open Problem: Has the world made a profit from this $25M investment yet? If not, how long will it take to get some ROI? $250M

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30 Open Problem: What kind of community is GD?

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31 The GD community Every node is a paper at the GD conference Edge from A to B if A cites B

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32 A high (academic) impact community Large indegree Influences other fields Fundamental area of research

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33 An engineering community Large outdegree Uses many other fields to produce solutions for problems ?Perhaps has commercial impact?

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34 An island community Not much connection to the outside ?Perhaps has no impact? ?Introspective community?

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35 Unsolved problem Open Problem: What kind of community is GD? Has its character changed over time? Can you show this in a picture (or a time-lapse animation) of citation network(s)? $10+

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36 Unsupported conjecture: Planarity has about 5 years to either live or die

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37 1930s: Fary Theorem Straight-line drawings exist 1960s: Tutte’s algorithm A straight-line drawing algorithm 1970s: Read’s algorithm Linear time straight-line drawing 1984: Tamassia algorithm Minimum number of bends 1987: Tamassia-Tollis algorithms Visibility drawing, upward planarity 1989: de Frassieux - Pach - Pollack Theorem Quadratic area straight-line drawing

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38 Conversation at GD1994, between an academic delegate and a industry delegate Industry delegate: “Why are you guys so obsessed with planarity? Most graphs that I want to draw aren’t planar.” Academic delegate: “Well, planarity is a central concept even for non-planar graphs. To be able to draw general graphs, we find a topology with a small number of edge crossings, model this topology as a planar graph, and draw that planar graph.” Industry delegate: “Sounds good. But I don’t know how to solve these sub-problems, for example, how to find a topology with a small number of crossings” Academic delegate: “These problems are fairly difficult and we don’t have perfect solutions. But we expect a few more years of research and we will get good results” Industry delegate: “Sounds good... I guess I’m looking forward to it”

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39 Mid 1990s: Mutzel’s thesis Crossing reduction by integer linear programming 1995: Purchase experiments Crossings really do inhibit understanding Late 1990s: Many beautiful papers on drawing planar graphs Good crossing reduction methods Early 2000s: Many more beautiful papers on drawing planar graphs............ Subjective Observation: The graph drawing community is obsessed with planarity. Plain lie: GD2010: More than 60% of papers are about planar graphs Almost true

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40 Interview with the CEO and CIO of a Graph Visualization company, Sept 15 2010 Interviewer: “Do you use planar graph drawing algorithms?” CEO: “No.” Interviewer: “Why not?” CEO: “Too much white space. Stability is a problem. Too difficult to integrate constraints. Incremental planar drawing doesn’t work well.” CIO:

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41 Interview with a Very Senior Software Engineer in a Very Large Company that has a Very Small Section that produces visualization software, Sept 23 2010 Interviewer: “Do your graph visualization tools use planar graph drawing algorithms?” Software Engineer: “Our customers want hierarchical layout first, and hierarchical layout second, and then they want hierarchical layout. We also have spring algorithms, but I’m not sure whether they use them.” Interviewer: “Yes, but maybe deep down in your software there is a planarity algorithm, or maybe a planar graph drawing algorithm?” Software Engineer: “No. No planarity.” Note: Yworks does use planar graph drawing algorithms

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42 Unsupported conjecture: Around 2015, either: Yworks wins a much larger market share, based on the competitive advantage of planarity-based methods, or Yworks finds that planarity-based methods are not useful, and drops the idea. Outlandish claim: Planarity-based methods are valuable, but need more time to prove themselves. Subjective observation: To know whether planar graph drawing is worthwhile:- We need to do lots more empirical work. We probably don’t need many more theorems.

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43 Outlandish Claim: The graph drawing community can contribute a lot to solving the scale problem

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44 Amount of data stored electronically 1950 1960 1970 1980 1990 2000

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45 04 05 06 07 08 09 350M 300M 250M 200M 150M 100M 50M 0 Social networks: Number of Facebook users

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46 The scale problem currently drives much of Computer Science Data sets are growing at a faster rate than the human ability to understand them. Businesses (and sciences) believe that their data sets contains useful information, and they want to get some business (or scientific) value out of these data sets.

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47 For Graph Drawing, there are two facets of the scale problem: 1. Computational complexity Efficiency Runtime We need more efficient algorithms 2. Visual complexity Effectiveness Readability We need better ways to untangle large graphs

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48 Graph Drawing has proposed three approaches to the scale problem: 1.Use 3D: spread the data over a third dimension 2.Use interaction: spread the data over time 3.Use clustering: view an abstraction of the data

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49 Well supported claim: 3D is almost dead

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50 Conversation between an Australian academic and a Canadian IBM research manager, 1992 IBM Research Manager: “Graphics cards capable of fast 3D rendering will soon become commodity items. They will give an unprecedented ability to draw diagrams in 3D. This is completely new territory.” Academic: “What?” IBM Research Manager: “Every PC will be able to do 3D. In IBM we do lots of graph drawing to model software. We think that 3D graph drawing will become commonplace.” Academic: “Really?” IBM Research Manager: “There’s more space in 3D, edge crossings can be avoided in 3D, navigation in 3D is natural”. Academic: “Really?” IBM Research Manager: “If you do a 3D graph drawing project, then IBM will fund it.” Academic: “Let’s do it!”

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51 1980s 2D Theorem: Every planar graph with maximum degree 4 admits a 2D orthogonal drawing with no edge crossings and at most 4 bends per edge.. P Eades, C Stirk, S Whitesides, The techniques of Komolgorov and Bardzin for three dimensional orthogonal graph drawings Information Processing Letters, 1996 A Papakostas, I Tollis, Incremental orthogonal graph drawing in three dimensions - Graph Drawing, 1997 - Springer P Eades, A Symvonis, S Whitesides, Three-dimensional orthogonal graph drawing algorithms, Discrete Applied Mathematics, 2000 DR Wood, Optimal three-dimensional orthogonal graph drawing in the general position model, Theoretical Computer Science, 2003 M Closson, S Gartshore, J Johansen, S Wismath, Fully dynamic 3-dimensional orthogonal graph drawing, Graph Drawing, 1999 TC Biedl, Heuristics for 3D-orthogonal graph drawings, Proc. 4th Twente Workshop on Graphs and …, 1995 G Di Battista, M Patrignani, F Vargiu, A split&push approach to 3D orthogonal drawing, Graph Drawing, 1998 D Wood, An algorithm for three-dimensional orthogonal graph drawing, Graph Drawing, 1998 M Patrignani, F Vargiu, 3DCube: A tool for three dimensional graph drawing, Graph Drawing, 1997 1996 3D Theorem: Every graph (even if it is nonplanar) with maximum degree 6 admits a 3D orthogonal drawing with no edge crossings and a constant number of bends per edge.

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52 Maurizio Patrignani 3D orthogonal drawing of K 7

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53 1980 1990 2000 2010 50% 100% Data source: none Quality of drawings 3D orthogonal graph drawing

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54 1990 – 2005: Many theorems on 3D Many metaphors Many research grants Many experiments A start-up company Mostly, 3D failed.

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55 2004 + : success with 2.5D? Colin Ware: “use 3D with a 2D attitude” Tim Dwyer: “use the third dimension for a single simple parameter (eg time)” SeokHee Hong: “Multiplane method”

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56 Tim Dwyer Market movement use the third dimension for a single simple parameter

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57 Multiplane method 1.Partition the graph 2.Draw each part on a 2D manifold in 3D 3.Connect the parts with inter-manifold edges Lanbo Zheng et al. Motifs in a protein-proteininteraction network

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58 Joshua Ho

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59 Multilevel visualization of clustered graphs (Feng, 1996) Draw the clusters on height i of the cluster tree on the plane z=i Draw on the plane z=0 Draw on the plane z=1 Draw on the plane z=2 The most cited paper in clustered graph drawing

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60 Unsupported conjecture: There is some hope of life for 2.5D graph drawing Unsupported conjecture: There are many interesting algorithmic and geometric problems for graph drawing in the multiplane style.

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61 Graph Drawing has proposed three approaches to the scale problem: 1.Use 3D: spread the data over a third dimension 2.Use interaction: spread the data over time 3.Use clustering: view an abstraction of the data

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62 Data Picture Graph visualization analysis The classical graph drawing pipeline the real world Action/decision

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63 In practice.. … … Data Picture Graph interaction visualization analysis Many iterations Action/decision the real world Action/decision Updates

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64 Interaction flow 1.The human looks at key frame F i. 2.The human thinks. 3.The human clicks on something. 4.System computes new key frame F i+1. 5.System computes in-betweening animation from key frame F i to key frame F i+1. 6.System displays animated transition from F i to F i+1. 7.i++ 8.Go to 1. Outrageous claim: all graph drawing algorithms need to be designed with interaction flow in mind

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65 Interaction can solve both problems: Computational complexity: The layout is only computed for the key frame (a relatively small graph) The “user think time” can be used for computation Visual complexity: At any one time, only a small graph is on the screen

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66 Interaction also raises some problems: Cognitive complexity: The user must remember stuff from one key frame to the next “mental map” problem Unsupported conjecture: Interaction flow poses many interesting problems for graph drawing

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67 Graph Drawing has proposed three approaches to the scale problem: 1.Use 3D: spread the data over a third dimension 2.Use interaction: spread the data over time 3.Use clustering: view an abstraction of the data

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68 A clustered graph C=(G,T) consists of a classical graph G, and a tree T such that the leaves of the tree T are the vertices of G. The tree T defines a clustering of the vertices of G.

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69 Data Picture Clustered Graph visualization clustering Clustered graph drawing pipeline

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70 Data Picture Clustered Graph Clustered graph drawing pipeline precis More precisely:-

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71 We can only draw a part of a huge graph at a time. What part shall we draw? A précis: a graph formed from an antichain in the cluster tree. A précis forms an abstraction of the data set.

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72 Melb Sydney Bris NSW Qld Australia Vic Monash LaTrobe MU UTS UNSW USyd UNE Wlng UQ QUT Griffith Deakin JCU

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73 UNE Wlng JCU Sydney Deakin Melb A précis is a graph, and can be drawn with the usual graph drawing algorithms Brisbane

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74 QUT Monash LaTrobe MU UTS UNSW USyd UNE Wlng UQ Griffith Deakin JCU MelbSydneyBris NSWQld Australia Vic A précis of a clustered graph is a graph defined by an antichain in the cluster tree

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75 Drill down The basic human interaction with a clustered graph The basic human interaction with a clustered graph is drill down: “Open” a node to see what it contains, that is, i.e, replace a node in the antichain with it’s children. Also, we need drill-up: “Close” a set of nodes to make the picture simpler i.e, replace a set of siblings in the antichain with their parent Note: In practical systems the human performs drill-down the system performs drill-up

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76 Data Picture Clustered Graph Clustered graph drawing pipeline precis Drill down interaction Unsubstantiated conjecture: Drill down/up are the only important interactions for large graphs. Outlandish claim: the Graph Drawing community can drive research into the algorithmics and combinatorial geometry of drill down/up interaction

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77 Michael Wybrow

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78 For interaction: “Drill down” on node X changes the size of X “Drill up” should be performed by the system, not by the user Nodes must move to accommodate change in size of node X The new picture must be nice in the usual graph drawing sense The mental map must be preserved: Preserve orthogonal ordering Preserve proximity Preserve topology Partially supported conjecture: Graph drawing researchers can design algorithms to give good drill down/up interaction

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79 Totally planar clustered graph drawing Say C is a clustered graph with cluster tree T=(V,E) and underlying graph G=(U,F). A drawing is a mapping p:V R 2 (edges are straight lines). A drawing is totally planar if For every node u of T, all vertices inside the convex hull of the descendents of u are descendents of u. And every précis is planar. 1 4 3 2 0 6 5 7 8 1 4 3 2 0 6 5 7 8 134 027 root 568

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80 1 4 3 2 0 6 5 7 8 Root Drill down 134027 568 planar

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81 1 4 3 2 0 6 5 7 8 Drill down 134 027 568 1 4 3 134027 568

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82 1 4 3 2 0 6 5 7 8 027 1 4 3 6 5 8 1 4 3 2 0 6 5 7 8 Drill down 027

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83 Open problem: Does every c-planar graph have a totally planar drawing? Open problem: Does every c-planar graph have straight-line multilevel drawing in which: Every level is planar The projection of a ith-level vertex onto level i-1 lies within the convex hull of its children Equivalently: Almost equivalently:

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84 Unsubstantiated claim: The only chance for a solution to the scale problem for graph drawing lies in the algorithmics and geometry of interaction and clusters

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85 Outrageous suggestion: Graph drawings are artworks

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86 A personal timeline Early 1980s: I used intuition and introspection to evaluate graph drawings Late 1980s: I read Shneiderman’s book Quality of an interface is a scientifically measurable function Task time, error rate, etc Now: I think graph drawings need to be beautiful as well as useful. Katy Borner, 2009: "In order to change behaviour, data graphics have to touch people intellectually and emotionally.“

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87 Visual Connections Sydney June 2008

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93 Outlandish claim: Graph drawings researchers have the skills needed to create graph drawing art

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94 George Birkoff, 1933: Beauty can be measured as a ratio M=O/C O = “order” ~= Kolmogorov complexity C = “complexity” ~= Shannon complexity Graph drawing problem as an optimization problem A number of objective functions f:Drawings RealNumber Given a graph G, find a drawing p(G) that optimizes f

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95 Unsupported conjecture: Using Birkoff-style functions, graph drawing algorithms can produce art.

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96 Size of Star represents the amount of email Each person is a star Social circle Distance between two stars represents closeness

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97 Currently: Graph drawing aims for 100% information display, and 0% art Outlandish suggestion: Graph drawing should have a range of methods, aiming for x% information display and (100-x)% art, for all 0 <= x <= 100

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98 Open problem: Use integer linear programming to produce valuable graph drawing art. $10 +

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99 Open problem: Why do force directed methods work?

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100 Force directed methods There have been many experiments A few more theorems would be good One theorem has been proved: If a graph has the right automorphisms, then there is a local minimum of a spring drawing that is symmetric. Some theory exists Combinatorial rigidity theory Theory of multidimensional scaling But there are many questions that I don’t know the answer Warning: this is introspective research!

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101 Open problem: What is the time complexity of a spring algorithm? Open problem: How many local minima are there? Open problem: How close are Euclidean distances to the graph theoretic distances? Open problem: Do force directed methods give bounded crossings most of the time?

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102 This is the end of the rhapsody of unsupported conjectures, subjective observations, outlandish claims, a few plain lies, and open problems

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103 Back to the main question: What is the future of Graph Drawing? Where does the road lead?

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104 Where does the road lead?

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108 Peter

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109 Question: What is the future of Graph Drawing?..... Sorry, I’ve run out of time.

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110 Question: What is the future of Graph Drawing? Answer: it’s up to you.

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111 Many thanks

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