Adaptive Greedy versus Non-adaptive Greedy for Influence Maximization

Abstract

We consider the *adaptive influence maximization problem*: given a network and a budget $k$, iteratively select $k$ seeds in the network to maximize the expected number of adopters. In the *full-adoption feedback model*, after selecting each seed, the seed-picker observes all the resulting adoptions. In the *myopic feedback model*, the seed-picker only observes whether each neighbor of the chosen seed adopts. Motivated by the extreme success of greedy-based algorithms/heuristics for influence maximization, we propose the concept of *greedy adaptivity gap*, which compares the performance of the adaptive greedy algorithm to its non-adaptive counterpart. Our first result shows that, for submodular influence maximization, the adaptive greedy algorithm can perform up to a $(1-1/e)$-fraction worse than the non-adaptive greedy algorithm, and that this ratio is tight. More specifically, on one side we provide examples where the performance of the adaptive greedy algorithm is only a $(1-1/e)$ fraction of the performance of the non-adaptive greedy algorithm in four settings: for both feedback models and both the *independent cascade model* and the *linear threshold model*. On the other side, we prove that in any submodular cascade, the adaptive greedy algorithm always outputs a $(1-1/e)$-approximation to the expected number of adoptions in the optimal non-adaptive seed choice. Our second result shows that, for the general submodular diffusion model with full-adoption feedback, the adaptive greedy algorithm can outperform the non-adaptive greedy algorithm by an unbounded factor. Finally, we propose a risk-free variant of the adaptive greedy algorithm that always performs no worse than the non-adaptive greedy algorithm.

26 pages, 0 figure, accepted at JAIR'22: Journal of Artificial Intelligence Research 74 (2022) 303-351; A short version of this paper was accepted at AAAI'20: Thirty-Fourth AAAI Conference on Artificial Intelligence

References in corpus (4)

• Influence Maximization: Near-Optimal Time Complexity Meets Practical Efficiency
• Adaptive Influence Maximization with Myopic Feedback
• On Adaptivity Gaps of Influence Maximization under the Independent Cascade Model with Full Adoption Feedback
• Don't Be Greedy: Leveraging Community Structure to Find High Quality Seed Sets for Influence Maximization