1. Data-Dependent Approximation
Lecture 1-5 Sandwich Method

2. Complexity Issues on DS Functions
Hardness of Decomposition and Approximation

3. Theorem
Proof

4. Proof

5. Theorem
Proof

7. Data Dependent Approximation
W. Lu, W. Chen, and L. V. Lakshmanan. From competition to complementarity: comparative inuence diusion and maximization. VLDB, 9(2):60-71, 2015.

8. Problem

9. Algorithm
Theorem

10. Proof

11. Activity Profit Maximization
Wang, Zhefeng, et al. "Activity Maximization by Effective Information Diffusion in Social Networks." IEEE Transactions on Knowledge and Data Engineering 29.11 (2017):

12. Problem

13. Examples

14. Examples

15. Upper Bound
Theorem

16. Lower Bound
Theorem

17. Algorithm
Theorem

18. Remark

19. Quality of Bounds Difference of Submodular functions! DS maximization!
Discrete DC maximization!
Difference of Convex functions!

20. Theoretical Foundation

21. Bound of Any Set Function

22. Quality of Bounds
Nonnegative !
Nonmonotone!
Submodular functions!

23. Modular Upper Bound

24. Thank You, end