H3: Laying Out Large Directed Graphs in 3D Hyperbolic Space - PowerPoint PPT Presentation

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H3: Laying Out Large Directed Graphs in 3D Hyperbolic Space

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H3: Laying Out Large Directed Graphs in 3D Hyperbolic Space Andrew Chan CPSC 533C March 24, 2003 H3 Ideas behind H3 Creating an optimal layout for a general graph is ... – PowerPoint PPT presentation

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Title: H3: Laying Out Large Directed Graphs in 3D Hyperbolic Space


1
H3 Laying Out Large Directed Graphs in 3D
Hyperbolic Space
  • Andrew Chan
  • CPSC 533C
  • March 24, 2003

2
H3
Image from http//graphics.stanford.edu/papers/h3
/fig/nab0.gif
3
Ideas behind H3
  • Creating an optimal layout for a general graph is
    tough
  • Creating an optimal layout for a tree is easier
  • Often it is possible to use domain-specific
    knowledge to create a hierarchical structure from
    a graph

4
Stumbling Blocks
  • The deeper the tree, the more nodes exponential
    growth
  • You can see an overview, or you can see fine
    details, but not both

5
Solution
  • A layout based on hyperbolic space, that allows
    for a focus context view
  • H3 used to lay out hierarchies of over 20 000
    nodes

6
Related Work
  • H3 has its roots in graph-drawing and
    focuscontext work

7
2D Graph and Tree Drawing
  • Thinking very small-scale
  • Frick, Ludwig, Mehldau created categories for
    graphs of nodes ranged from 16 in the smallest
    category, to gt 128 in the largest

8
2D Tree Drawing (contd)
MosiacG System Zyers and Stasko Image
from http//www.w3j.com/1/ayers.270/paper/270.htm
l
9
3D Graph Drawing
SGI fsn file-system viewer Image
from http//www.sgi.com/fun/images/fsn.map2.jpg
10
3D Graph Drawing (contd)
  • Other work centered around the idea of a
    mass-spring system
  • Node repel one another, but links attract
  • Difficulty in converging when you try to scale
    the systems
  • Aside Eric Brochu is doing similar work in 2D -
    http//www.cs.ubc.ca/ebrochu/mmmvis.htm

11
3D Tree Drawing
Cone Trees, Robertson, Mackinlay, Card Image
from http//www2.parc.com/istl/projects/uir/pubs/
items/UIR-1991-06-Robertson-CHI91-Cone.pdf
12
Hyperbolic FocusContext
Hyperbolic Tree Browser, Lamping, Rao Image
from http//www.acm.org/sigchi/chi95/Electronic/d
ocumnts/papers/jl_figs/strip1.htm
13
Alternate Geometry
  • Information at http//cs.unm.edu/joel/NonEuclid/
  • Euclidean geometry
  • 3 angles of a triangle add up to?
  • Shortest distance between two points?
  • Spherical geometry
  • How we think about the world
  • Shortest way from Florida to Philippines?

14
Alternate Geometry (contd)
  • Hyperbolic Geometry / Space
  • Is important to the Theory of Relativity
  • The fifth dimension
  • Can be projected into 2-D as a pseudosphere
  • Key As a point moves away from the center
    towards the boundary circle, its distance
    approaches infinity

15
H3s Layout
Image from http//graphics.stanford.edu/papers/h3
/fig/nab0.gif
16
Finding a Tree from a Graph
  • Most effective if you have domain-specific
    knowledge
  • Examples
  • File system
  • Web site structure
  • Function call graphs

17
Tree Layout
Cone tree layout versus H3 Layout Image from
http//graphics.stanford.edu/papers/h3/html/node12
.htmconefig
18
Sphere Packing
  • Need an effective way to place information
  • Cannot place spheres randomly
  • Want to have a fast algorithm

19
Sphere Packing (contd)
Image from http//graphics.stanford.edu/papers/h3
/fig/incrhemi.gif
20
Demo
21
Strengths
  • Can easily see what the important structures are
    and the relationships between them
  • Can let you ignore noise in data
  • Animated transitions
  • Responsive UI

22
Weaknesses
  • Starting view only uses part of the sphere
  • Moving across the tree can disorient you cost of
    clicking on the wrong place is high
  • Labels not present if node too far from center

23
Questions?
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