Chayant Tantipathananandh

1
Constant-Factor Approximation Algorithms for
Identifying Dynamic Communities

• Chayant Tantipathananandh
• with Tanya Berger-Wolf

2
Social Networks
These are snapshots and networks change over time
3
Dynamic Networks
t1
t1
t2

t2
5
2
3
4
1
5
2
4
1

5
2
3
4
3
2
1
4
5

• Interactions occur in the form of disjoint groups
• Groups are not communities

4
Communities

• What is community?
• Cohesive subgroups are subsets of actors among
  whom there are relatively strong, direct,
  intense, frequent, or positive ties. Wasserman
  Faust 1994
• Dynamic Community Identification
• GraphScope Sun et al 2005
• Metagroups Berger-Wolf Saia 2006
• Dynamic Communities TBK 2007
• Clique Percolation Palla et al 2007
• FacetNet Lin et al 2009
• Bayesian approach Yang et al 2009

5
Ship of Theseus
from Wikipedia
The ship was preserved by the Athenians ,
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.
Plutarch, Theseus

• Jeannot's knife has had its blade changed
  fifteen times and its handle fifteen times, but
  is still the same knife. French story

6
Ship of Theseus
Individual parts never change identities
Cost for changing identity

7
Ship of Theseus
Identity changes to match the group
Costs for visiting and being absent

8
Approach
9
Community Color
Valid coloring In each time step, different
groups have different colors.
10
Interpretation

• Group color
• How does community c interact at time t?

11
Interpretation
Individual color Who belong to community c at
time t?
1
2
1
2
2
1
2
1
2
1
12
Social Costs Conservatism
2
2
a
a
2
2
a
a
2
2
2
2
a
a
2
2

• Switching cost a

Absence cost ß1
Visiting cost ß2
13
Social Costs Loyalty
3
3
ß1
ß1
ß1
3
2
2
ß1
3
ß1
1
ß1
1
ß1
Absence cost ß1
Visiting cost ß2
Switching cost a
14
Social Costs Loyalty
ß2
3
ß2
3
ß2
2
ß2
2
Switching cost a
Absence cost ß1
Visiting cost ß2
15
Problem Complexity

• Minimizing total cost is hardNP-complete and
  APX-hard with Berger-Wolf and Kempe 2007
• Constant-Factor Approximation details in paper
• Easy special caseIf no missing individuals and
  2a ß2 , thensimply weighted bipartite
  matchingdetails in paper

16
Greedy Approximation
No visiting or absence and minimizing switching
time
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Greedy Approximation
No visiting or absence and minimizing switching
3
4
2
maximizing path coverage
3
Greedy alg guaranteesmax2, 2a/ß1, 4a/ß2 in a,
ß1, ß2, independent of input size
7
2
3
4
Improvement by dynamic programming
3
time
18
Southern Women Data Set DGG 1941

• 18 individuals, 14 time steps
• Collected in Natchez, MS, 1935

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Ethnography DGG1941
Core
Core
note columns not ordered by time
20
Optimal Communities
individuals
time
Core
Core
ethnography
all costs equal white circles unknown
21
Approximate
Optimal
time
time
ethnography
22
Approximation Power
28 inds, 44 times
29 inds, 82 times
313 inds, 758 times
23
Approximation Power
41 inds, 418 times
264 inds, 425 times
96 inds, 1577 times
24
Conclusions

• Identity of objects that change over time (Ship
  of Theseus Paradox)
• Formulate an optimization problem
• Greedy approximation
• Fast
• Near-optimal
• Future Work
• Algorithm with guarantee not depending on a, ß1,
  ß2
• Network snapshots instead of disjoint groups

25
Thank You

• NSF grant, KDD student travel award

Mayank Lahiri
Chayant
Jared Saia
David Kempe
Arun Maiya
Ilya Fischoff
Habiba
Saad Sheikh
Tanya Berger-Wolf
Dan Rubenstein
Anushka Anand
Siva Sundaresan
Rajmonda Sulo
Robert Grossman