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Fractional Budget Allocation for Influence Maximization under General Marketing Strategies

Akhil Bhimaraju, Eliot W. Robson, Lav R. Varshney, Abhishek K. Umrawal

TL;DR

This work addresses fractional influence maximization under general marketing strategies by allowing each node's activation probability to be an increasing affine function of its discount, with a total budget constraint. It develops a generalized discrete-greedy algorithm that handles heterogeneous $f_v(y_v)=a_v y_v + b_v$ and proves a $(1-1/e)$-approximation guarantee, with polynomial-time complexity $O(|V|^2 T)$ where $T$ is the cost of evaluating the diffusion objective. The key contribution is extending prior continuous and homogeneous models to heterogeneous linear activations while maintaining scalability and submodular optimization guarantees. Empirical results on real-world networks show the method is scalable and robust to varying $f_v$, performing comparably to baselines and enabling practical deployment in large social networks.

Abstract

We consider the fractional influence maximization problem, i.e., identifying users on a social network to be incentivized with potentially partial discounts to maximize the influence on the network. The larger the discount given to a user, the higher the likelihood of its activation (adopting a new product or innovation), who then attempts to activate its neighboring users, causing a cascade effect of influence through the network. Our goal is to devise efficient algorithms that assign initial discounts to the network's users to maximize the total number of activated users at the end of the cascade, subject to a constraint on the total sum of discounts given. In general, the activation likelihood could be any non-decreasing function of the discount, whereas, our focus lies on the case when the activation likelihood is an affine function of the discount, potentially varying across different users. As this problem is shown to be NP-hard, we propose and analyze an efficient (1-1/e)-approximation algorithm. Furthermore, we run experiments on real-world social networks to show the performance and scalability of our method.

Fractional Budget Allocation for Influence Maximization under General Marketing Strategies

TL;DR

This work addresses fractional influence maximization under general marketing strategies by allowing each node's activation probability to be an increasing affine function of its discount, with a total budget constraint. It develops a generalized discrete-greedy algorithm that handles heterogeneous and proves a -approximation guarantee, with polynomial-time complexity where is the cost of evaluating the diffusion objective. The key contribution is extending prior continuous and homogeneous models to heterogeneous linear activations while maintaining scalability and submodular optimization guarantees. Empirical results on real-world networks show the method is scalable and robust to varying , performing comparably to baselines and enabling practical deployment in large social networks.

Abstract

We consider the fractional influence maximization problem, i.e., identifying users on a social network to be incentivized with potentially partial discounts to maximize the influence on the network. The larger the discount given to a user, the higher the likelihood of its activation (adopting a new product or innovation), who then attempts to activate its neighboring users, causing a cascade effect of influence through the network. Our goal is to devise efficient algorithms that assign initial discounts to the network's users to maximize the total number of activated users at the end of the cascade, subject to a constraint on the total sum of discounts given. In general, the activation likelihood could be any non-decreasing function of the discount, whereas, our focus lies on the case when the activation likelihood is an affine function of the discount, potentially varying across different users. As this problem is shown to be NP-hard, we propose and analyze an efficient (1-1/e)-approximation algorithm. Furthermore, we run experiments on real-world social networks to show the performance and scalability of our method.
Paper Structure (5 sections, 1 theorem, 6 equations, 6 figures, 1 table, 1 algorithm)

This paper contains 5 sections, 1 theorem, 6 equations, 6 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Mathematical Model
  3. Approximation algorithm with constant-factor guarantee
  4. Experiments
  5. Conclusion

Key Result

Theorem 1

When the functions $f_v(\cdot)$ are all nonnegative increasing linear functions, i.e., $f_v(y_v)=a_vy_v+b_v$ with $a_v,b_v\ge0$, the output $y$ of Alg. alg:discrete-greedy-general satisfies where $y^*$ is the optimal solution of eq:cont-optimization. Further, Alg. alg:discrete-greedy-general runs in $O\left(|V|^2T\right)$, where $T$ is the time complexity of computing $\sigma(\cdot)$.

Figures (6)

  • Figure 1: Facebook network
  • Figure 2: Wikipedia network
  • Figure 3: Deezer network
  • Figure 5: Facebook network
  • Figure 6: Wikipedia network
  • ...and 1 more figures

Theorems & Definitions (1)

  • Theorem 1