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

TL;DR

This paper addresses time-critical influence maximization in social networks by extending classical models to include time delays, proposing efficient heuristics that outperform existing methods while maintaining influence spread quality.

Contribution

It introduces time-delayed IC and LT models for influence maximization, proving submodularity and developing fast heuristics that match greedy algorithm performance.

Findings

Heuristic algorithms achieve similar influence spread as greedy algorithms.

Proposed methods are significantly faster than traditional greedy approaches.

Algorithms outperform existing heuristics that ignore time delays.

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.