1 the future of graph drawing and a rhapsody peter eades

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The Future of Graph Drawing

and a rhapsody

Peter Eades

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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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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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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

worldNote: Fundamental

research (“theory”) is usually inspired by the real world

extroverted research

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A brief history

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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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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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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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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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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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Subjective Observation:

Graph Drawing is successful

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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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“Graph Drawing is the big success story in information visualization”

Stephen North, September 2010

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Subjective Observation:

Graph Drawing is connected to many other disciplines

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Virtual Environments

Case Study - Stock Market

MS-Guidelines

MS-Process

MS-Taxonomy

Software Engineering

Human Perception

Information Display

Data Mining

Abstract Datamany applicationslarge

ABSTRACT DATA

SOFTWARE ENGINEERING

VIRTUAL ENVIRONMENTS

HUMAN PERCEPTION

DATA MINING

MS-TAXONOMY

INFORMATION DISPLAY

CASE STUDY

MS-GUIDELINES

MS-PROCESS

finding patterns

human perceptual tools

virtual abstract worlds

virtual hybrid worlds

data characterisatio

n

task analysis

virtual real worlds

new user-interface technology

increase human-computer bandwidth

many interaction styles

physiology

sensory interaction

sensory bias

perceptual data mining

multi-attributed

cognition

automated intelligent tools

visual data mining

information visualisation

information haptisation

information sonification

hearing hapticsvision

information metaphors

VE platform

s

spatial metaphors

direct metaphors

temporal metaphors

guidelines for perceptionguidelines for

MS-Taxonomy

guidelines for spatial metaphors

guidelines for direct metaphors

guidelines for temporal metaphors

abstraction

quality principles

designprocess

architecture

taxonomy

guidelinesstructure

iterative prototyping

design guidelines

finding trading rules

stock market data

technical analysis

display mapping

prototyping

evaluation

expert heuristicevaluation

summativeevaluation

formativeevaluation

i-CONE

process structure

Haptic Workbench

ResponsiveWorkbench

WEDGE

Barco Baron

mapping temporal metaphors

mapping direct metaphors

mapping spatial metaphors

3D bar chart

moving average surface

bidAsk landscape

haptic 3D bar charthaptic moving average surfaceauditory bidAsk landscape

consider software platform

consider hardware platform

guidelines for information display

information perceptualisation

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

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GraphDrawing

GraphicArt

Alg

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ms

HCID

ataMin

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om

pu

ter

Gra

ph

ics

Co

mp

utatio

nal

Geo

metry

CombinatorialGeometry

LinearAlgebra

InfoVis

GraphTheory

Graph Drawing:

ConnectionsVisualLanguages ComputerScience

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Biology

SocialNetworksComputer

Science

SecurityGraphDrawing

DataMining

InfoVis

HD

DataVis

Finance

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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

GraphDrawing

GraphicAr

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LinearAlgebra

Info

Vis

GraphTheory

Graph Drawing: Connecti

ons

VisualLanguages

$10+

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GraphDrawing

GraphicAr

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LinearAlgebra

Info

Vis

GraphTheory

Graph Drawing: Connecti

ons

VisualLanguages

Unsolved problem: Create algorithms and systems to draw (ordered) hypergraphs in the metro-map metaphor.

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Outlandish claim:Graph Drawing is dying

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Interview with a Very Experienced Industry Researcher in a Telco, Sept 14, 2010

<suddenly> “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: <thinking>

…

<60 seconds of silence>

…

<more thinking>

“For force directed methods, visual complexity is now a problem ….”

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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: <thinking>

…

<60 seconds of silence>

…

<looks worried>

…

<more thinking>

…

“No”

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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: <thinking in silence>

....

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: <Smiles, knowing that nested drawings have been around much longer> “Anything else?”

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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: <interrupts> “Yes, but I guess that kind of thing didn’t come from the Graph Drawing research community?”

CEO: “Oh, I guess not.”

…

<thinking>

…

CIO: “I don’t think we have used any of the other results. They are certainly interesting, but ...”

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Data source: citeceer

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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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Open Problem:Is it worth the

money?

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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

$250M

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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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Open Problem:What kind of community is GD?

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

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

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

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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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Unsupported conjecture:

Planarity has about 5 years to either live or die

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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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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: <cheerily> “Sounds good ... I guess I’m looking forward to it”

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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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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: <laughs>

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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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Unsupported conjecture: Around 2015, either:Yworks wins a much larger market share, based on the competitive advantage of planarity-based methods, orYworks 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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Outlandish Claim:

The graph drawing community can contribute a lot to solving the scale problem

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Am

ount

of d

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ed

elec

tron

ical

ly

1950 1960 1970 1980 1990 2000

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04 05 06 07 08 09

350M

300M

250M

200M

150M

100M

50M

0

Social networks: Number of Facebook users

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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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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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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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Well supported claim:

3D is almost dead

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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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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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Ma

uri

zio

Pat

rig

na

ni

3D orthogonal drawing of K7

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1980 1990 2000 2010

50%

100%

Data source: none

Quality of d

rawings

3D orthogonal graph drawing

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1990 – 2005: Many theorems on 3D Many metaphors Many research grants Many experiments A start-up company

Mostly, 3D failed.

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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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Tim Dwyer

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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.

Mo

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a p

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in-p

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intera

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ork

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Joshua Ho

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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



The most cited paper in clustered graph drawing

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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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Data PictureGraphvisualizationanalysis

The classical graph drawing pipeline

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In practice . . … …

Data PictureGraph

interaction

visualizationanalysis

Many iterations

Action/decisionthe real world

Action/decisionUpdates

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Interaction flow

1. The human looks at key frame Fi.

2. The human thinks.

3. The human clicks on something.

4. System computes new key frame Fi+1.

5. System computes in-betweening animation from key frame Fi

to key frame Fi+1.

6. System displays animated transition from Fi to Fi+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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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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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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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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Data PictureClustered

Graphvisualizationclustering

Clustered graph drawing pipeline

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Graph


precis

More precisely:-

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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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Sydney

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Deakin

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A précis is a graph, and can be drawn with the usual graph drawing algorithms

Brisbane

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A précis of a clustered graph is a graph defined by an antichain in the cluster tree

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Drill down

The basic human interaction with a clustered graphThe 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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Graph


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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Michael Wybrow

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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 orderingPreserve proximityPreserve topology

Partially supported conjecture: Graph drawing researchers can design algorithms to give good drill down/up interaction

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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:VR2 (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

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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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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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Outrageous suggestion:

Graph drawings are artworks

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A personal timeline

Early 1980s: I used intuition and introspection to evaluate graph drawings

Late 1980s: I read Shneiderman’s bookQuality of an interface is a scientifically

measurable functionTask 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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Visual ConnectionsSydneyJune 2008

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Outlandish claim:

Graph drawings researchers have the skills needed to create graph drawing

art

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George Birkoff, 1933: Beauty can be measured as a ratio M=O/C

O = “order” ~= Kolmogorov complexityC = “complexity” ~= Shannon complexity

Graph drawing problem as an optimization problem A number of objective functions

f:DrawingsRealNumber Given a graph G, find a drawing p(G) that

optimizes f

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

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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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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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Open problem: Use integer linear programming to produce valuable graph drawing art.

$10+

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Open problem:

Why do force directed methods work?

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

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Where does the road lead?

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Peter

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.....

Sorry, I’ve run out of time.

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Answer: it’s up to you.

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Many thanks

1 the future of graph drawing and a rhapsody peter eades

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