Time-Critical Influence Maximization in Social Networks with Time-Delayed Diffusion Process (1204.3074v3)

Abstract: Influence maximization is a problem of finding a small set of highly influential users, also known as seeds, in a social network such that the spread of influence under certain propagation models is maximized. In this paper, we consider time-critical influence maximization, in which one wants to maximize influence spread within a given deadline. Since timing is considered in the optimization, we also extend the Independent Cascade (IC) model and the Linear Threshold (LT) model to incorporate the time delay aspect of influence diffusion among individuals in social networks. We show that time-critical influence maximization under the time-delayed IC and LT models maintains desired properties such as submodularity, which allows a greedy approximation algorithm to achieve an approximation ratio of $1-1/e$. To overcome the inefficiency of the greedy algorithm, we design two heuristic algorithms: the first one is based on a dynamic programming procedure that computes exact influence in tree structures and directed acyclic subgraphs, while the second one converts the problem to one in the original models and then applies existing fast heuristic algorithms to it. Our simulation results demonstrate that our algorithms achieve the same level of influence spread as the greedy algorithm while running a few orders of magnitude faster, and they also outperform existing fast heuristics that disregard the deadline constraint and delays in diffusion.

Time-Critical Influence Maximization in Social Networks with Time-Delayed Diffusion Process

The paper "Time-Critical Influence Maximization in Social Networks with Time-Delayed Diffusion Process" by Wei Chen, Wei Lu, and Ning Zhang tackles the problem of maximizing influence spread in social networks within a specified time deadline. The motivation stems from real-world scenarios like viral marketing campaigns where timing is crucial, such as short-term sales promotions where influence needs to propagate rapidly to meet a temporal objective.

Overview of Models and Problem

Addressing the problem of influence maximization, wherein the objective is to select a seed set of influential nodes to maximize influence propagation in a network, the authors extend two classical models: the Independent Cascade (IC) model and the Linear Threshold (LT) model to include time constraints and diffusion delays. The resulting models, denoted as IC-M (Independent Cascade with Meeting events) and LT-M (Linear Threshold with Meeting events), incorporate meeting probabilities between nodes, reflecting the time delays in real social interactions.

The core challenge is to maintain the submodularity of influence spread, which ensures that greedy approximation algorithms can be effectively used to approximate the optimal seed set with a (1 - 1/e) approximation guarantee. The authors prove that their extensions to the IC and LT models retain these desirable mathematical properties, despite the added complexity of time delays and meeting events.

Proposed Algorithms

Key contributions of the paper include two heuristic algorithms, MIA-M and MIA-C, for the IC-M model, and the LDAG-M algorithm for the LT-M model. These algorithms aim to improve the scalability and efficiency of influence maximization under time constraints:

1. MIA-M and MIA-C: MIA-M uses dynamic programming to compute exact influence spread within the maximum influence arborescence (MIA) context, while MIA-C converts the problem by estimating propagation probabilities that combine meeting events, influence events, and the deadline.
2. LDAG-M: For the LT-M model, the Local Directed Acyclic Graph (LDAG) approach is adapted, enabling efficient computation of influence spread by constructing small, effective influence regions in the network.

The evaluation of these algorithms, via simulations on real dataset networks like NetHEPT and WikiVote, shows that they can run significantly faster than the greedy approximation algorithm while achieving comparable levels of influence spread.

Implications and Future Work

This research has significant implications for applications in viral marketing, information dissemination, and other domains where quick influence spread is critical. The modeling approach allows for a more realistic reflection of the time-sensitive nature of such processes in real-world networks.

Potential future work could explore further optimization of these heuristic approaches, integration with additional real-world datasets to test robustness, and extension of time-critical modeling to encompass even more complex scenarios involving negative propagation or competition within the network.

In summary, this paper makes a meaningful contribution by extending established influence maximization models to handle time-critical constraints efficiently, offering practical algorithms with solid performance in both speed and influence quality.