Adversarial Influence Blocking Maximization (AIBM) aims to select a set of positive seed nodes that propagate synchronously with the known negative seed nodes to counteract their negative influence. Time factor plays a particularly vital role for many AIBM application scenarios. However, the AIBM problem with time constraint remains unexplored. More importantly, existing AIBM studies have not thoroughly investigated the submodularity of the objective function, thereby failing to establish a theoretical approximation guarantee. To address these challenges, firstly, we establish the Time-Critical Adversarial Influence Blocking Maximization (TC-AIBM), which explicitly incorporates time constraint. Then, we provide a theoretical proof of the submodularity of the TC-AIBM objective function under three different tie-breaking rules. Finally, a Bidirectional Influence Sampling (BIS) algorithm is proposed to solve the TC-AIBM problem. Leveraging the monotonicity and submodularity of the objective function, BIS achieves an approximation guarantee of $(1-1/e-ε)(1-ψ)$. Comprehensive experiments on four real-world datasets demonstrate that the proposed BIS algorithm exhibits excellent robustness across various negative seeds, time constraint, and tie-breaking rules, outperforming state-of-the-art baselines. In addition, BIS is up to three orders of magnitude faster than the Greedy algorithm.

翻译：对抗影响力阻断最大化（AIBM）旨在选取一组正向种子节点，使其与已知负向种子节点同步传播，以抵消后者的负面影响力。时间因素在许多AIBM应用场景中尤为关键。然而，具有时间约束的AIBM问题尚未得到探索。更重要的是，现有AIBM研究未能深入探究目标函数的子模性，因此无法建立理论近似保证。针对这些挑战，首先，我们建立了时间关键型对抗影响力阻断最大化（TC-AIBM）问题，明确引入了时间约束。然后，在三种不同的打破平局规则下，我们提供了TC-AIBM目标函数子模性的理论证明。最后，提出了一种双向影响力采样（BIS）算法来求解TC-AIBM问题。利用目标函数的单调性和子模性，BIS实现了$(1-1/e-ε)(1-ψ)$的近似保证。在四个真实数据集上的全面实验表明，所提出的BIS算法在不同负向种子、时间约束和打破平局规则下展现出优异的鲁棒性，优于最先进的基线方法。此外，BIS算法的速度比贪心算法快三个数量级。