1. Lecture 2-6 Complexity for Computing Influence Spread
Ding-Zhu Du

2. Section 9.1-2

3. Definition

4. Examples

5. Turing Reduction

6. Oracle DTM
Query tape
Query
state

7. Oracle DTM
Query tape
answer
state
Remark:

8. #P-Complete

9. Theorem (Chen et al., 2010)
Proof

11. 1 2 3

12. 1 1 2 3 2 3 1 1 2 3 2 3

13. 1 1 2 3 2 3 1 1 2 3 2 3

14. Theorem (Chen et al., 2010)
Proof

17. Disadvantage Lack of efficiency.
Computing σm(S) is # P-hard under both IC and LT models.
Selecting a new vertex u that provides the largest marginal gain σm(S+u) - σm(S), which can only be approximated by Monte-Carlo simulations (10,000 trials).
Assume a weighted social graph as input.
How to learn influence probabilities from history?
( Step 3 of the Greedy algorithm above)

18. References

19. Thanks, end.