Chayant Tantipathananandh with Tanya Berger-Wolf

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 t=1 t=1 3 5 4 1 2 t=2 1 … 3 2 t=2 5 2 3 4 1 5 2 4 1 … 5 2 3 4 4 5 5 2 4 1 3 Aggregated network 1 1 2 2 3 5 2 3 • Interactions occur in the form of disjoint groups • Groups are not communities 1 1 4

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 Switching cost α 2 2 α α 2 2 α α 2 2 2 2 α α 2 2 Absence cost β1 Visiting cost β2

13. Social Costs: Loyalty 3 3 β1 β1 β1 2 3 2 3 β1 β1 1 1 β1 β1 Switching cost α Absence cost β1 Visiting cost β2

14. Social Costs: Loyalty β2 3 β2 3 β2 2 β2 2 Switching cost α Absence cost β1 Visiting cost β2

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 2α ≤ β2 , thensimply weighted bipartite matching[details in paper]

16. Greedy Approximation No visiting or absence and minimizing switching time

17. Greedy Approximation No visiting or absence and minimizing switching 3 4 2 ≈ maximizing path coverage 3 Greedy alg guaranteesmax{2, 2α/β1, 4α/β2} in α, β1, β2, independent of input size 7 2 3 4 Improvementby dynamic programming 3 time

18. Southern Women Data Set [DGG 1941] • 18 individuals, 14 time steps • Collected in Natchez, MS, 1935 aggregated network

19. 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 Core Core Core Core

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 α, β1, β2 • 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