1. Tantipathananandh Chayant Tantipathananandh with Tanya Berger-Wolf Constant-Factor Approximation Algorithms for Identifying Dynamic Communities

2. Social Networks These are snapshots and networks change over time

3. Dynamic Networks Aggregated network 5 4 3 2 1 1 32 2 1 1 Interactions occur in the form of disjoint groups Groups are not communities … t=2 t=1 32145 54 3 12 52341 5234 5241 … t=2 5 4 1 2 3

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

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 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2

12. Social Costs: Conservatism Switching cost α α α α Absence cost β 1 Visiting cost β 2 α α α 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

13. Social Costs: Loyalty β1β1 β1β1 β1β1 Absence cost β 1 Visiting cost β 2 Switching cost α β1β1 β1β1 β1β1 2 2 3 3 3 3 1 1 1 1 3 3 2 2 3 3 β1β1

14. Social Costs: Loyalty β2β2 β2β2 Switching cost αAbsence cost β 1 Visiting cost β 2 2 2 3 3 β2β2 2 2 β2β2 3 3

15. Problem Complexity Minimizing total cost is hard NP-complete and APX-hard [with Berger-Wolf and Kempe 2007] Constant-Factor Approximation [details in paper] Easy special case If no missing individuals and 2α ≤ β 2, then simply weighted bipartite matching [details in paper]

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

17. Greedy Approximation 2 4 3 3 7 3 3 4 ≈ maximizing path coverage No visiting or absence and minimizing switching No visiting or absence and minimizing switching 2 Improvement by dynamic programming Greedy alg guarantees max{2, 2α/β 1, 4α/β 2 } in α, β 1, β 2, independent of input size Greedy alg guarantees max{2, 2α/β 1, 4α/β 2 } in α, β 1, β 2, independent of input size time

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

19. Ethnography [DGG1941] Core note: columns not ordered by time

20. Optimal Communities all costs equal white circles = unknown Core time individuals ethnography

21. time Approximate Optimal Core ethnography

22. Approximation Power 28 inds, 44 times29 inds, 82 times313 inds, 758 times

23. Approximation Power 41 inds, 418 times264 inds, 425 times96 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, β 1, β 2 – Network snapshots instead of disjoint groups

25. Arun Maiya Saad Sheikh Thank You NSF grant, KDD student travel award Habiba David Kempe Jared Saia Mayank Lahiri Dan Rubenstein Tanya Berger-Wolf Rajmonda Sulo Robert Grossman Siva Sundaresan Ilya Fischoff Anushka Anand Chayant