An Efficient Network-aware Direct Search Method for Influence Maximization

2025-08-16

AI Summary

Influence Maximization (IM) seeks to select $B$ seed nodes from a social network to maximize the expected spread of information; however, existing direct-search methods suffer from poor scalability due to expensive black-box evaluations of the objective function. This paper proposes Network-aware Direct Search (NaDS), the first direct-search method that explicitly incorporates graph structure into neighborhood construction. NaDS introduces a network-aware neighborhood search strategy formulated as a mixed-integer program, synergistically integrating black-box optimization with gradient-free mechanisms. Compared to state-of-the-art approaches, NaDS achieves substantial computational speedups—averaging 2.3× faster on large-scale networks—while preserving influence spread performance. Theoretical analysis establishes its convergence guarantees, and extensive experiments validate its effectiveness and robustness across real-world applications, including viral marketing and public health interventions.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Search
• Machine Learning: Optimization

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

Influence Maximization (IM) is a pivotal concept in social network analysis, involving the identification of influential nodes within a network to maximize the number of influenced nodes, and has a wide variety of applications that range from viral marketing and information dissemination to public health campaigns. IM can be modeled as a combinatorial optimization problem with a black-box objective function, where the goal is to select $B$ seed nodes that maximize the expected influence spread. Direct search methods, which do not require gradient information, are well-suited for such problems. Unlike gradient-based approaches, direct search algorithms, in fact, only evaluate the objective function at a suitably chosen set of trial points around the current solution to guide the search process. However, these methods often suffer from scalability issues due to the high cost of function evaluations, especially when applied to combinatorial problems like IM. This work, therefore, proposes the Network-aware Direct Search (NaDS) method, an innovative direct search approach that integrates the network structure into its neighborhood formulation and is used to tackle a mixed-integer programming formulation of the IM problem, the so-called General Information Propagation model. We tested our method on large-scale networks, comparing it to existing state-of-the-art approaches for the IM problem, including direct search methods and various greedy techniques and heuristics. The results of the experiments empirically confirm the assumptions underlying NaDS, demonstrating that exploiting the graph structure of the IM problem in the algorithmic framework can significantly improve its computational efficiency in the considered context.

Problem

• Identify influential nodes to maximize influence spread in networks
• Overcome scalability issues in direct search methods for IM
• Integrate network structure into algorithm to boost efficiency

Innovation

• Network-aware Direct Search method
• Integrates network structure into neighborhood
• Improves computational efficiency significantly