Effective submodularity of influence maximization on temporal networks

TL;DR

This paper demonstrates that influence maximization on temporal networks, despite the non-submodular nature of the influence function, can be effectively approached with greedy algorithms that behave as if the function were submodular.

Contribution

The study shows that greedy optimization strategies perform well on temporal networks, behaving as if the influence function were submodular, with minimal violations observed in real networks.

Findings

Violations of submodularity conditions are rare in real networks.

Greedy solutions are close to optimal, within the guaranteed optimality gap.

Greedy optimization is effective for influence maximization on temporal networks.

Abstract

We study influence maximization on temporal networks. This is a special setting where the influence function is not submodular, and there is no optimality guarantee for solutions achieved via greedy optimization. We perform an exhaustive analysis on both real and synthetic networks. We show that the influence function of randomly sampled sets of seeds often violates the necessary conditions for submodularity. However, when sets of seeds are selected according to the greedy optimization strategy, the influence function behaves effectively as a submodular function. Specifically, violations of the necessary conditions for submodularity are never observed in real networks, and only rarely in synthetic ones. The direct comparison with exact solutions obtained via brute-force search indicate that the greedy strategy provides approximate solutions that are well within the optimality gap guaranteed for strictly submodular functions. Greedy optimization appears therefore an effective strategy for the maximization of influence on temporal networks.