# Minimizing the Influence of Misinformation via Vertex Blocking

## TL;DR

This paper addresses the influence minimization of misinformation in social networks, proving the problem's NP-hardness, and introduces efficient algorithms that outperform existing methods significantly in large-scale scenarios.

## Contribution

It is the first to prove the NP-hardness of the influence minimization problem and proposes novel algorithms with graph sampling and dominator trees for efficient large-scale solutions.

## Key findings

- Algorithms are up to 6 orders of magnitude faster than state-of-the-art.
- Proposed algorithms achieve better effectiveness with comparable or lower time costs.
- Extensive experiments on real graphs validate the efficiency and effectiveness of the methods.

## Abstract

Information cascade in online social networks can be rather negative, e.g., the spread of rumors may trigger panic. To limit the influence of misinformation in an effective and efficient manner, the influence minimization (IMIN) problem is studied in the literature: given a graph G and a seed set S, blocking at most b vertices such that the influence spread of the seed set is minimized. In this paper, we are the first to prove the IMIN problem is NP-hard and hard to approximate. Due to the hardness of the problem, existing works resort to greedy solutions and use Monte-Carlo Simulations to solve the problem. However, they are cost-prohibitive on large graphs since they have to enumerate all the candidate blockers and compute the decrease of expected spread when blocking each of them. To improve the efficiency, we propose the AdvancedGreedy algorithm (AG) based on a new graph sampling technique that applies the dominator tree structure, which can compute the decrease of the expected spread of all candidate blockers at once. Besides, we further propose the GreedyReplace algorithm (GR) by considering the relationships among candidate blockers. Extensive experiments on 8 real-life graphs demonstrate that our AG and GR algorithms are significantly faster than the state-of-the-art by up to 6 orders of magnitude, and GR can achieve better effectiveness with its time cost close to AG.