Influence Minimization via Blocking Strategies

TL;DR

This work tackles influence minimization by blocking up to $b$ nodes or edges to minimize the expected spread from a seed set in diffusion on graphs. It introduces AdvancedGreedy, a sampling-based framework that leverages dominator trees to estimate the impact of blockers with near-linear time, achieving a $(1-1/e-\varepsilon)$-approximation under the Linear Threshold model and substantial speedups over Monte Carlo-based methods. It also proposes GreedyReplace, a heuristic that improves solution quality under the IC model by considering out-neighbors and replacements in a guided manner. Empirical results on real networks show speedups of about three orders of magnitude with competitive or superior effectiveness, highlighting practical scalability for timely intervention against misinformation or epidemics.

Abstract

We study the influence minimization problem: given a graph $G$ and a seed set $S$, blocking at most $b$ nodes or $b$ edges such that the influence spread of the seed set is minimized. This is a pivotal yet underexplored aspect of network analytics, which can limit the spread of undesirable phenomena in networks, such as misinformation and epidemics. Given the inherent NP-hardness of the problem under the IC and LT models, previous studies have employed greedy algorithms and Monte Carlo Simulations for its resolution. However, existing techniques become cost-prohibitive when applied to large networks due to the necessity of enumerating all the candidate blockers and computing the decrease in expected spread from blocking each of them. This significantly restricts the practicality and effectiveness of existing methods, especially when prompt decision-making is crucial. In this paper, we propose the AdvancedGreedy algorithm, which utilizes a novel graph sampling technique that incorporates the dominator tree structure. We find that AdvancedGreedy can achieve a $(1-1/e-ε)$-approximation in the problem under the LT model. Experimental evaluations on real-life networks reveal that our proposed algorithms exhibit a significant enhancement in efficiency, surpassing the state-of-the-art algorithm by three orders of magnitude, while achieving high effectiveness.

Figures (7)

• Figure 1: A toy graph $G$, where $v_1$ is the seed node and the value on each edge indicates its propagation probability
• Figure 2: Sampled graphs of the graph $G$ in Figure \ref{['fig:sample']}.
• Figure 3: Dominator trees of the sampled graphs in Figure \ref{['fig:sample-example']}.
• Figure 4: DESC($G,s,\theta$)
• Figure 5: DESCE($G,s,\theta$)

Theorems & Definitions (17)

• Definition 1: activation probability
• Definition 2: expected spread
• Definition 3: IMIN problem
• Definition 4: IMIN-EB problem
• Example 1
• Lemma 1
• Corollary 1
• Theorem 1
• Theorem 2
• Definition 5: dominator