Data-Dependent Approximation Lecture 1-5 Sandwich Method

Complexity Issues on DS Functions Hardness of Decomposition and Approximation

Theorem Proof

Proof

Theorem Proof

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.

Problem

Algorithm Theorem

Proof

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): 2374-2387.

Problem

Examples

Examples

Upper Bound Theorem

Lower Bound Theorem

Algorithm Theorem

Remark

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

Theoretical Foundation

Bound of Any Set Function

Quality of Bounds Nonnegative ! Nonmonotone! Submodular functions!

Modular Upper Bound

Thank You, end