Approximation Algorithms for Budget Splitting in Multi-Channel Influence Maximization

2026-04-01

AI Summary

This study addresses the budget allocation problem across multiple advertising channels—such as billboards and social networks—and presents the first formal model capturing inter-channel interaction effects on overall influence. The resulting influence function is non-submodular, prompting the development of an approximation framework based on the submodularity ratio and generalized curvature. The authors propose a randomized greedy algorithm and a two-stage adaptive strategy to optimize allocations under this setting. They establish the first theoretical approximation guarantee for such non-submodular influence maximization, achieving an approximation ratio of $\frac{1}{\alpha}(1 - e^{-\gamma \alpha})$. Extensive experiments on real-world datasets demonstrate that the proposed methods significantly outperform existing approaches in enhancing total influence.

Abstract

How to utilize an allocated budget effectively for branding and promotion of a commercial house is an important problem, particularly when multiple advertising media are available. There exist multiple such media, and among them, two popular ones are billboards and social media advertisements. In this context, the question naturally arises: how should a budget be allocated to maximize total influence? Although there is significant literature on the effective use of budgets in individual advertising media, there are hardly any studies examining budget allocation across multiple advertising media. To bridge this gap, this paper introduces the \textsc{Budget Splitting Problem in Billboard and Social Network Advertisement}. We introduce the notion of \emph{interaction effect} to capture the additional influence due to triggers from multiple media of advertising. Using this notion, we propose a noble influence function $Φ(,)$ that captures the total influence and shows that this function is non-negative, monotone, and non-bisubmodular. We introduce \emph{bi-submodularity ratio $(γ)$} and \emph{generalized curvature $(α)$} to measure how close a function is to being bi-submodular and how far a function is from being modular, respectively. We propose the Randomized Greedy and Two-Phase Adaptive Greedy approach, where the influence function is non-bisubmodular and achieves an approximation guarantee of $\frac{1}α\left(1-e^ {-γα} \right)$. We conducted several experiments using real-world datasets and observed that the proposed solution approach's budget splitting leads to a greater influence than existing approaches.

Problem

• Budget Allocation
• Influence Maximization
• Multi-Channel Advertising
• Interaction Effect
• Billboard and Social Media

Innovation

• budget splitting
• interaction effect
• non-bisubmodular optimization
• approximation algorithm
• multi-channel influence maximization