Adaptive Influence Blocking: Minimizing the Negative Spread by Observation-Based Policies

Spread of negative influence (N-Inf) in a networked system seems to be inevitable, e.g., epidemic spread in human networks, rumors in an online social network and computer virus plaguing the Internet etc. The widespread of N-Inf might cause severe damage and hence the Influence Blocking (IB) problem is attracting ample research interest. The IB problem aims at minimizing the N-Inf spread by immunization, i.e. selecting k (budget size) immunization nodes (Imm-nodes) to prevent the N-Inf from spreading. However, existing works for IB problem are all formulated as a one-shot task: selecting all the k Imm-nodes at the very beginning of N-Inf spread. In real world, unforeseen events might occur and one-shot policies will lack reserved measures to handle these situations. A more reasonable policy is to adaptively invest the budget based on the observation of N-Inf spread along as the time goes by. With the adaptive policy, we can both reserve resources for handling unforeseen events and save unnecessary costs if the spread of N-Inf dies out quickly. Motivated by the above considerations, we propose a novel Adaptive Influence Blocking (AIB) problem. Given the intermediate observations of N-Inf spread, the AIB problem aims at selecting Imm-nodes adaptively. We design a k-R (k-nodes-per-Round) policy which selects k Imm-nodes for each round until the budget is exhausted, and an α-T (α-Tolerance) policy which selects a new Imm-node if the expected N-Inf spread exceeds a threshold α. Scalable algorithms with provable approximation guarantees and error bounds are implemented for these policies and significant improvements on time complexity are achieved. Experimental results on real-world datasets demonstrate the effectiveness and scalability of the proposed methods.