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1
The Future of Graph Drawing
and a rhapsody
Peter Eades
2
Question: What is the future of Graph Drawing?
Answer: ... I’ll tell you later ...
But first: some constraints, and a brief history ....
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
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
worldNote: Fundamental
research (“theory”) is usually inspired by the real world
extroverted research
5
A brief history
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
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
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
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
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
11
Subjective Observation:
Graph Drawing is successful
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
13
“Graph Drawing is the big success story in information visualization”
Stephen North, September 2010
14
Subjective Observation:
Graph Drawing is connected to many other disciplines
15
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
16
GraphDrawing
GraphicArt
Alg
orith
ms
HCID
ataMin
ing C
om
pu
ter
Gra
ph
ics
Co
mp
utatio
nal
Geo
metry
CombinatorialGeometry
LinearAlgebra
InfoVis
GraphTheory
Graph Drawing:
ConnectionsVisualLanguages ComputerScience
17
Biology
SocialNetworksComputer
Science
SecurityGraphDrawing
DataMining
InfoVis
HD
DataVis
Finance
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
GraphDrawing
GraphicAr
t
Alg
ori
thm
s
HCI
Da
taM
inin
g
Co
mp
ute
rG
rap
hic
s
Co
mp
uta
tion
alG
eo
me
try
CombinatorialGeometry
LinearAlgebra
Info
Vis
GraphTheory
Graph Drawing: Connecti
ons
VisualLanguages
$10+
19
GraphDrawing
GraphicAr
t
Alg
ori
thm
s
HCI
Da
taM
inin
g
Co
mp
ute
rG
rap
hic
s
Co
mp
uta
tion
alG
eo
me
try
CombinatorialGeometry
LinearAlgebra
Info
Vis
GraphTheory
Graph Drawing: Connecti
ons
VisualLanguages
Unsolved problem: Create algorithms and systems to draw (ordered) hypergraphs in the metro-map metaphor.
20
Outlandish claim:Graph Drawing is dying
21
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 ….”
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: <thinking>
…
<60 seconds of silence>
…
<looks worried>
…
<more thinking>
…
“No”
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: <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?”
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: <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 ...”
25
Data source: citeceer
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.
27
Open Problem:Is it worth the
money?
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
$250M
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
30
Open Problem:What kind of community is GD?
31
The GD community• Every node is a paper at the GD conference• Edge from A to B if A cites B
32
A high (academic) impact community• Large indegree• Influences other fields• Fundamental area of research
33
An engineering community• Large outdegree• Uses many other fields to produce solutions for problems• ?Perhaps has commercial impact?
34
An island community• Not much connection to the outside• ?Perhaps has no impact?• ?Introspective community?
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+
36
Unsupported conjecture:
Planarity has about 5 years to either live or die
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
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: <cheerily> “Sounds good ... I guess I’m looking forward to it”
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
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: <laughs>
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
42
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.
43
Outlandish Claim:
The graph drawing community can contribute a lot to solving the scale problem
44
Am
ount
of d
ata
stor
ed
elec
tron
ical
ly
1950 1960 1970 1980 1990 2000
45
04 05 06 07 08 09
350M
300M
250M
200M
150M
100M
50M
0
Social networks: Number of Facebook users
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.
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
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
49
Well supported claim:
3D is almost dead
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!”
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.
52
Ma
uri
zio
Pat
rig
na
ni
3D orthogonal drawing of K7
53
1980 1990 2000 2010
50%
100%
Data source: none
Quality of d
rawings
3D orthogonal graph drawing
54
1990 – 2005: Many theorems on 3D Many metaphors Many research grants Many experiments A start-up company
Mostly, 3D failed.
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”
56
Tim Dwyer
Ma
rke
t m
ov
emen
t
us
e th
e t
hir
d d
imen
sio
n f
or
a s
ing
le
sim
ple
par
ame
ter
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.
Mo
tifs in
a p
rote
in-p
rote
in
intera
ctio
n n
etw
ork
58
Joshua Ho
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
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.
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
62
Data PictureGraphvisualizationanalysis
The classical graph drawing pipeline
63
In practice . . … …
Data PictureGraph
interaction
visualizationanalysis
Many iterations
Action/decisionthe real world
Action/decisionUpdates
64
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
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
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
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
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.
69
Data PictureClustered
Graphvisualizationclustering
Clustered graph drawing pipeline
70
Data PictureClustered
Graph
Clustered graph drawing pipeline
precis
More precisely:-
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.
72
Melb
Sydney
Bris
NSW
QldAustralia
Vic
Monash
LaTrobe
MUUTS
UNSW
USyd
UNE
Wlng
UQ
QUT
GriffithDeakin
JCU
73
UNE
Wlng
JCU
Sydney
Deakin
Melb
A précis is a graph, and can be drawn with the usual graph drawing algorithms
Brisbane
74
QU
T
Mo
nas
h
LaT
rob
e
MU
UT
S
UN
SW
US
yd
UN
E
Wln
g
UQ
Gri
ffit
h
Dea
kin
JCU
Melb Sydney Bris
NSW Qld
Australia
Vic
A précis of a clustered graph is a graph defined by an antichain in the cluster tree
75
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
76
Data PictureClustered
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
77
Michael Wybrow
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 orderingPreserve proximityPreserve topology
Partially supported conjecture: Graph drawing researchers can design algorithms to give good drill down/up interaction
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: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
43
2
0
65
7
8
1
43
2
0
65
7
8
134 027
root
568
80
1
43
2
0
65
7
8
RootDrill down
134 027
568
planar
81
1
43
2
0
65
7
8
Drill down 134027
568
1
43
134 027
568
82
1
43
2
0
65
7
8
027
1
43
65
8
1
43
2
0
65
7
8
Drill down 027
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:
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
85
Outrageous suggestion:
Graph drawings are artworks
86
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.“
87
Visual ConnectionsSydneyJune 2008
88
89
90
91
92
93
Outlandish claim:
Graph drawings researchers have the skills needed to create graph drawing
art
94
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
95
Unsupported conjecture: Using Birkoff-style functions, graph drawing algorithms can produce art.
96
Size of Star represents the amount of email
Each person is a star
Social circle
Distance between two stars represents closeness
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
98
Open problem: Use integer linear programming to produce valuable graph drawing art.
$10+
99
Open problem:
Why do force directed methods work?
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!
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?
102
This is the end of the rhapsody of unsupported conjectures, subjective observations, outlandish claims, a few plain lies, and open problems
103
Back to the main question: What is the future of Graph Drawing? Where does the road lead?
104
Where does the road lead?
105
106
107
108
Peter
109
Question: What is the future of Graph Drawing?
.....
Sorry, I’ve run out of time.
110
Question: What is the future of Graph Drawing?
Answer: it’s up to you.
111
Many thanks