Given a graph G, a budget k and a misinformation seed set S, Influence Minimization (IMIN) via node blocking aims to find a set of k nodes to be blocked such that the expected spread of S is minimized. This problem finds important applications in suppressing the spread of misinformation and has been extensively studied in the literature. However, existing solutions for IMIN still incur significant computation overhead, especially when k becomes large. In addition, there is still no approximation solution with non-trivial theoretical guarantee for IMIN via node blocking prior to our work. In this paper, we conduct the first attempt to propose algorithms that yield data-dependent approximation guarantees. Based on the Sandwich framework, we first develop submodular and monotonic lower and upper bounds for our non-submodular objective function and prove the computation of proposed bounds is \#P-hard. In addition, two advanced sampling methods are proposed to estimate the value of bounding functions. Moreover, we develop two novel martingale-based concentration bounds to reduce the sample complexity and design two non-trivial algorithms that provide (1-1/e-\epsilon)-approximate solutions to our bounding functions. Comprehensive experiments on 9 real-world datasets are conducted to validate the efficiency and effectiveness of the proposed techniques. Compared with the state-of-the-art methods, our solutions can achieve up to two orders of magnitude speedup and provide theoretical guarantees for the quality of returned results.

翻译：给定图G、预算k及错误信息种子集S，基于节点阻断的影响力最小化（IMIN）旨在寻找需阻断的k个节点，使得S的预期传播范围最小化。该问题在抑制错误信息传播中具有重要应用，并已在文献中得到广泛研究。然而，现有IMIN解决方案仍存在显著计算开销，尤其在k值较大时。此外，在本文工作之前，基于节点阻断的IMIN尚无具有非平凡理论保证的近似解。本文首次尝试提出能提供数据依赖近似保证的算法。基于Sandwich框架，我们首先为非子模目标函数建立子模且单调的下界与上界，并证明所提边界函数的计算复杂度为#P-hard。同时，提出两种先进采样方法来估计边界函数值。进一步，我们开发两种新颖的基于鞅的浓度界以减少样本复杂度，并设计两种非平凡算法，为边界函数提供(1-1/e-ε)近似解。在9个真实数据集上的综合实验验证了所提技术的效率与有效性。与现有最优方法相比，我们的方案可实现高达两个数量级的加速，并为返回结果的质量提供理论保证。