Zebras
Dan Rubenstein, Siva Sandaresan, Ilya Fischhoff (Princeton)
Movie credit: “Champions of the Wild”, Omni-Film Productions.
Ants
Stephen Pratt (Princeton)
People – Hidden Groups
Baumes et al. (RPI)
What’s a group?
• Zebras – harems, herds, physically close
collection of individuals
• Ants – ants being carried by a scout
• People – families, friends, collection of
individuals with a common goal, sexual
contacts, individuals at the same
location
file
4
1
3
9
1
4
4
4
4
8
1
9
8
9
4
4
2
1
t=3
t=4
3
2
t=1
t=2
3
1
1
Theseus’s Paradox
• During a twelve month period 95% of all the
atoms that make up your 50 trillion cells are
replaced
• FAA regulations: airplane = left rudder
number
• Ship of Theseus
"The ship wherein Theseus and the youth of Athens returned [from
Crete] had thirty oars, and was preserved by the Athenians down even
to the time of Demetrius Phalereus, for they took away the old planks
as they decayed, putting in new and stronger timber in their place,
insomuch that this ship became a standing example among the
philosophers, for the logical question of things that grow; one side
holding that the ship remained the same, and the other contending that
it was not the same."
What is persistence?
A group is persistent (stable) if it is
there all the time
A group is persistent if some (big)
fraction β of it exists some (big)
fraction α of time (recurs regularly?)
overlap (X,Y) 
2|X Y |
|X ||Y |
4/5
4/5
4/5
4/5
4/5
4
1
9
16/17
3
1
1
t=1
2/3
4
1
4
1
4
8
1
1
8
16/17
9
3
6/7
4
1
4
2
11
2
2/3
1
β=.9 t=3
t=2 β=.5
t=4
2
1
3
4
10
5
9
8
7
6
Time
Time step
step =
=4
1 seconds
second
1
2
3
4
3/4
0
5
2
6
3
7
4
8
5
3/4
0
9
3
10
4
1
5
2
6
3/4
0
3
4
4
5
5
6
6
7
3/4
0
7
5
8
6
9
7
10
8
How do we get the groups?
• Zebra – photos, sensor collars (ZebraNet)
physical proximity
• Ants – video marking
physical proximity
• People:
–
–
–
–
–
Report of personal contacts (epidemiology)
Cell phone communication
Computer communication
Intelligence information (database queries)
Simulations
Zebras (Ants, People) - Clustering
Objects within a cluster are closer to each
other than to objects in other clusters
Clustering
Joachim M. Buhmann, Department of Computer Science ETH Zurich
People – Connected Components
Baumes et al.(RPI) and Washington Post
Jan-Dec 2001
2000
Aug-Sep
Jan-Apr
May-Jul
2001
Pentagon
Pennsylvania
WTC North
WTC South
hard
easy
Great! But…
There are millions of people, groups
change constantly – finding groups
is COMPUTATIONALLY EXPENSIVE
• Given a group – is it persistent?
• To what persistent groups does a
given individual belong?
• I know persistent groups are no
bigger than 100. Find them?
• I know there is exactly one
persistent group. Can you find it?
Credits:
Dan Rubenstein
Siva Sundaresan
Ilya Fischhoff
Jared Saia
Simon Levin
S. Muthu
Muthukrishana
Martin Pal