Scalable Fair Influence Blocking Maximization via Approximately Monotonic Submodular Optimization

TL;DR

This work tackles fairness in Influence Blocking Maximization under Demographic Parity (DP) by introducing a DP-aware objective that preserves a tractable approximate submodular structure. The authors define a DP surrogate $\,\mathcal{W}$ and combine it with the blocking objective $\,\mathcal{F}$ through a scalarization $\mathcal{K}(S_P)=\beta\,\mathcal{W}(S_P)+(1-\beta)\,\mathcal{F}(S_P)$, enabling efficient optimization under $(\kappa,\epsilon)$-approximate submodularity. They develop CELF-R, an accelerated seed selection algorithm that uses Naive VRR Path Sampling and a robust lazy greedy strategy, and they demonstrate the ability to construct Pareto fronts by varying $\beta$. Experiments on four real-world networks show that CELF-R achieves a $(1-1/e-\psi)$-approximate solution with substantial efficiency gains over LP-based baselines, providing scalable, fair protection across communities. Overall, the paper offers a practical framework for fair IBM with tunable fairness–effectiveness trade-offs and empirical Pareto-front construction.

Abstract

Influence Blocking Maximization (IBM) aims to select a positive seed set to suppress the spread of negative influence. However, existing IBM methods focus solely on maximizing blocking effectiveness, overlooking fairness across communities. To address this issue, we formalize fairness in IBM and justify Demographic Parity (DP) as a notion that is particularly well aligned with its semantics. Yet enforcing DP is computationally challenging: prior work typically formulates DP as a Linear Programming (LP) problem and relies on costly solvers, rendering them impractical for large-scale networks. In this paper, we propose a DP-aware objective while maintaining an approximately monotonic submodular structure, enabling efficient optimization with theoretical guarantees. We integrate this objective with blocking effectiveness through a tunable scalarization, yielding a principled fairness-effectiveness trade-offs. Building on this structure, we develop CELF-R, an accelerated seed selection algorithm that exploits approximate submodularity to eliminate redundant evaluations and naturally supports Pareto front construction. Extensive experiments demonstrate that CELF-R consistently outperforms state-of-the-art baselines, achieving a $(1-1/e-ψ)$-approximate solution while maintaining high efficiency.

Figures (5)

• Figure 1: A toy example on Karate Club network.
• Figure 2: Overview of CELF-R and Pareto Front Construction. CELF-R consists of two main components: (a) Naive VRR path sampling, which estimates node-level blocking contributions and supports efficient evaluation of the trade-off objective $\mathcal{K}$; and (b) a robust lazy greedy selection strategy that explicitly models bounded deviations under approximate submodularity. By sweeping the trade-off parameter $\beta$, CELF-R produces a set of solutions that collectively form an empirical Pareto front balancing fairness and blocking effectiveness.
• Figure 3: Comparison of different fairness notions on the FIBM problem. The x-axis denotes blocking effectiveness $\mathcal{F}$, and the y-axis denotes the fairness-aware objective $\mathcal{W}$, where higher values are better for both. Our method produces a Pareto front by varying the trade-off parameter $\beta$, while each baseline yields a single solution. Points closer to the top-right corner indicate better fairness–effectiveness trade-offs.
• Figure 4: Ablation study on seed selection strategies. Pareto fronts produced by CELF-R and Full Computation (FC) nearly overlap, indicating that CELF-R achieves solution quality comparable to exhaustive marginal gain evaluation. In contrast, CELF performs significantly worse due to its assumption of strict submodularity.
• Figure 5: Computational efficiency comparison between CELF-R and Full Computation (FC). The y-axis reports the total number of marginal gain evaluations $\Lambda$ at each iteration $i$.

Theorems & Definitions (17)

• Definition 1: Fair Influence Blocking Maximization, FIBM
• Definition 2: $(\kappa, \epsilon)$-approximately monotonic submodular
• Lemma 1
• Lemma 2
• Lemma 3
• Lemma 4
• Theorem 1
• Lemma 4
• proof
• Lemma 4