Transcript Drawing Clustered Graphs

The Future of Graph Drawing
and a rhapsody
Peter Eades
1
Question: What is the future of Graph Drawing?
Answer: ... I’ll tell you later ...
But first: some constraints, and a brief history ....
2
Two different motivations for research
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
Constraint: This talk is mostly aimed at extroverts
3
What is the relationship between extroverted
research and the real world?
extroverted research
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
4
A brief history
5
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
6
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
7
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
8
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
9
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
10
Subjective Observation:
Graph Drawing is successful
11
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
12
“Graph Drawing is the big success story
in information visualization”
Stephen North, September 2010
13
Subjective Observation:
Graph Drawing is connected
to many other disciplines
14
Keith Nesbitt 2003: use metro map metaphor for abstract data connections
many
applications
large
ABSTRACT
DATA
Abstract Data
Virtual Environments
Data Mining
MS-Taxonomy
Information Display
MS-Guidelines
Human Perception
MS-Process
Software Engineering
Case Study - Stock
Market
HUMAN
PERCEPTION
multiattributed
finding
patterns
DATA
MINING
visual
data
mining
VIRTUAL
ENVIRONMENT
S
new user-interface
technology
many
interaction
styles INFORMATION
DISPLAY
increase humancomputer bandwidth
virtual real
worlds
SOFTWARE
CASE
ENGINEERING
STUDY
finding
trading
rules
perceptual
data
mining
information
visualisation
information
haptisation
virtual
abstract
worlds
VE
platforms
virtual
hybrid
worlds
guidelines
for information information
perceptualisation
display
stock
market
data
guidelines guidelines for
structure MSTaxonomy
data
characterisation
MS-GUIDELINES
consider
software
platform
guidelines
for perception
process
structure
task
analysis
consider
hardware
platform
MS-TAXONOMY
guidelines guidelines
for spatial for direct
metaphors metaphors
iterative
prototyping
MSPROCESS
information
sonification
display
mapping
guidelines
for
temporal
metaphors
mapping mapping mapping
spatial
direct
temporal
metaphors metaphors metaphors
summativ
e
evaluation
formative
evaluation
i-CONE
Barco Baron
Responsive
Workbenc
h
Haptic
Workbench
WEDGE
prototyping
expert
heuristic
evaluation
evaluation
3D bar
chart
moving
average
surface
bidAsk
landscape
haptic
3D bar
chart
haptic
moving
average
surface
auditory
bidAsk
landscape
15
Info
Vis
Computer
Graphics
DataMining
GraphDrawing
HCI
Computer
Science
Algorithms
Computational
Geometry
VisualLanguages
Graph Drawing:
Connections
CombinatorialGeometry
GraphTheory
LinearAlgebra
16
Biology
Computer
Science
Security
GraphDrawing
Social
Networks
Finance
17
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 coauthored by people in different
communities
Graph
Drawing:
Connection
s
Algori
thms
VisualLan
guages
Computa
tional
Geometr
y
H
C
I
Data
Minin
g
GraphD
rawing
Inf
o
Vis
Comp
uter
Graph
ics
$10+
CombinatorialG
eometry
GraphTh
eory
LinearA
lgebra
18
Graph
Drawing:
Connection
s
Algori
thms
VisualLan
guages
Computa
tional
Geometr
y
H
C
I
Data
Minin
g
GraphD
rawing
Inf
o
Vis
Comp
uter
Graph
ics
Unsolved problem: Create
algorithms and systems to
draw (ordered) hypergraphs in
the metro-map metaphor.
CombinatorialG
eometry
GraphTh
eory
LinearA
lgebra
19
Outlandish claim:
Graph Drawing is dying
20
Interview with a Very Experienced Industry Researcher in
a Telco, Sept 14, 2010
Interviewer: “What are the most useful results from the
Graph Drawing researchers in the last ten years?”
Industry Researcher: <thinking>
…
<60 seconds of silence>
…
<suddenly> “Scale! Those force directed
algorithms run much faster now than
they did around 2000, using the
Koren/Quigley/Walshaw methods!”
<more thinking>
“For force directed methods, visual complexity is
now a problem ….”
21
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”
22
Interview with the CEO and CTO of a Graph Drawing
software company, Sept 15, 2010
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.”
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>
....
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?”
23
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 ...”
24
GD Conference: Citations
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
GD
Data source: citeceer
25
100%
85%
50%
Unsubstantiated claim: the quality of graph
drawings isn’t getting any better.
1980
1990
2000
2010
Data source: none
26
Open Problem:
Is it worth the
money?
27
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
$250M
Open Problem:
Has the world made a profit from this
$25M investment yet? If not, how
long will it take to get some ROI?
28
100%
85%
Open Problem:
Has the world made a profit from this
$25M investment yet? If not, how
long will it take to get some ROI?
1980
1990
2000
2010
29
Open Problem:
What kind of community is GD?
30
The GD community
• Every node is a paper at the GD conference
• Edge from A to B if A cites B
31
A high (academic) impact community
• Large indegree
• Influences other fields
• Fundamental area of research
32
An engineering community
• Large outdegree
• Uses many other fields to produce solutions for problems
• ?Perhaps has commercial impact?
33
An island community
• Not much connection to the outside
• ?Perhaps has no impact?
• ?Introspective community?
34
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)?
35
Unsupported conjecture:
Planarity has about 5 years to
either live or die
36
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
37
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”
38
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:
Plain lie:
The graph drawing community is
GD2010: More than 60% of
obsessed with planarity.
papers are about planar graphs
39
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>
40
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
41
Outlandish claim:
Planarity-based methods are
valuable, but need more time
to prove themselves.
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.
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.
42
Outlandish Claim:
The graph drawing community can
contribute a lot to solving the scale problem
43
1950
1960
1970
1980
1990
2000
44
350M
300M
Social networks:
 Number of Facebook users
250M
200M
150M
100M
50M
0
04
05
06
07
08
09
45
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.
46
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
47
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
48
Well supported claim:
3D is almost dead
49
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!”
50
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
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.
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
51
Maurizio Patrignani
3D orthogonal
drawing of K7
52
100%
3D orthogonal graph drawing
50%
1980
1990
2000
2010
Data source: none
53
1990 – 2005:
 Many theorems on 3D
 Many metaphors
 Many research grants
 Many experiments
 A start-up company
Mostly, 3D failed.
54
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”
55
Tim Dwyer
56
Market movement
use the third dimension for a single
simple parameter
Multiplane method
1. Partition the graph
2. Draw each part on a 2D manifold in 3D
3. Connect the parts with inter-manifold edges
Motifs in a protein-protein
interaction network
Lanbo Zheng et al.
57
Joshua Ho
58
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=2
Draw on the
plane z=1
Draw on the
plane z=0
The most cited paper in clustered graph drawing
59
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.
60
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
61
The classical graph drawing pipeline
Data
analysis
Graph
visualization
Picture
Action/decision
the real world
62
In practice . . … …
Many iterations
Data
analysis
Graph
visualization
Picture
interaction
Updates
Action/decision
the real worldAction/decision
63
Interaction flow
1.
2.
3.
4.
5.
The human looks at key frame Fi.
The human thinks.
The human clicks on something.
System computes new key frame Fi+1.
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
64
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
65
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
66
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
67
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.
68
Clustered graph drawing pipeline
Data
clustering
Clustered
Graph
visualization
Picture
69
Clustered graph drawing pipeline
More precisely:-
Data
Clustered
Graph
precis
Picture
70
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.
71
Australia
Qld
Vic
JCU
Bris
UQ
QUT
Griffith
Deakin
Melb
LaTrobe
UNE
Wlng
UTS
USyd
MU
Monash
NSW
UNSW
Sydney
72
A précis is a graph, and can be drawn with the usual graph drawing
algorithms
JCU
Brisbane
Deakin
Melb
UNE
Sydney
Wlng
73
Australia
NSW
UQ
Bris
JCU
UNSW
UTS
USyd
UNE
Wlng
Deakin
Sydney
MU
Monash
LaTrobe
Melb
Qld
Griffith
Vic
QUT
A précis of a
clustered graph
is a graph
defined by an
antichain in the
cluster tree
74
Drill down
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
75
Clustered graph drawing pipeline
Data
Clustered
Graph
precis
Picture
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
76
Michael Wybrow
77
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
Partially supported conjecture:
 Preserve topology
Graph drawing researchers can
design algorithms to give good
drill down/up interaction
78
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R2 (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.
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Root
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Drill down 134
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82
Open problem: Does every c-planar graph
have a totally planar drawing?
Equivalently: Almost equivalently:
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
83
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
84
Outrageous
suggestion:
Graph drawings are
artworks
85
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.“
86
Visual Connections
Sydney
June 2008
87
88
89
90
91
92
Outlandish claim:
Graph drawings researchers have the skills
needed to create graph drawing art
93
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
94
Unsupported conjecture: Using Birkoff-style functions,
graph drawing algorithms can produce art.
95
Size of Star
represents the
amount of email
Social circle
Each person
is a star
Distance between two
stars represents
closeness
96
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
97
Open problem: Use integer linear programming
to produce valuable graph drawing art.
98
Open problem:
Why do force directed methods work?
99
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
100
Open problem:
How many local
minima are there?
Open problem:
How close are Euclidean
distances to the graph
theoretic distances?
Open problem:
What is the time complexity
of a spring algorithm?
Open problem:
Do force directed methods give
bounded crossings most of the time?
101
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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Question: What is the future of Graph Drawing?
.....
Sorry, I’ve run out of time.
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Question: What is the future of Graph Drawing?
Answer: it’s up to you.
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Many thanks
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