A fractional memory-efficient approach for online continuous-time influence maximization

Influence maximization (IM) under a continuous-time diffusion model requires finding a set of initial adopters which when activated lead to the maximum expected number of users becoming activated within a given amount of time. State-of-the-art approximation algorithms applicable to solving this intractable problem use reverse reachability influence samples to approximate the diffusion process. Unfortunately, these algorithms require storing large collections of such samples which can become prohibitive depending on the desired solution quality, properties of the diffusion process and seed set size. To remedy this, we design an algorithm that allows the influence samples to be processed in a streaming manner, avoiding the need to store them. We approach IM using two fractional objectives: a fractional relaxation and a multi-linear extension of the original objective function. We derive a progressively improved upper bound to the optimal solution, which we empirically find to be tighter than the best existing upper bound. This enables instance-dependent solution quality guarantees that are observed to be vastly superior to the theoretical worst case. Leveraging these, we develop an algorithm that delivers solutions with a superior empirical solution quality guarantee at comparable running time with greatly reduced memory usage compared to the state-of-the-art. We demonstrate the superiority of our approach via extensive experiments on five real datasets of varying sizes of up to 41M nodes and 1.5B edges.