# Influence Maximization: Near-Optimal Time Complexity Meets Practical Efficiency

arXiv: https://arxiv.org/abs/1404.0900 · HTML: https://mlsanity.com/paper/1404.0900/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2014.

## Built on by (most cited first, 30 of 33)

- [Deep Graph Representation Learning and Optimization for Influence Maximization](https://mlsanity.com/paper/2305.02200/) (2023)
- [A Survey on Influence Maximization: From an ML-Based Combinatorial Optimization](https://mlsanity.com/paper/2211.03074/) (2022)
- [ToupleGDD: A Fine-Designed Solution of Influence Maximization by Deep Reinforcement Learning](https://mlsanity.com/paper/2210.07500/) (2022)
- [LeNSE: Learning To Navigate Subgraph Embeddings for Large-Scale Combinatorial Optimisation](https://mlsanity.com/paper/2205.10106/) (2022)
- [Combinatorial Bandits under Strategic Manipulations](https://mlsanity.com/paper/2102.12722/) (2021)
- [IM-META: Influence Maximization Using Node Metadata in Networks With Unknown Topology](https://mlsanity.com/paper/2106.02926/) (2021)
- [Influence Maximization via Graph Neural Bandits](https://mlsanity.com/paper/2406.12835/) (2024)
- [Socialbots on Fire: Modeling Adversarial Behaviors of Socialbots via Multi-Agent Hierarchical Reinforcement Learning](https://mlsanity.com/paper/2110.10655/) (2021)
- [Identifying Influential Users in Unknown Social Networks for Adaptive Incentive Allocation Under Budget Restriction](https://mlsanity.com/paper/2107.05992/) (2021)
- [Contextual Combinatorial Bandits with Changing Action Sets via Gaussian Processes](https://mlsanity.com/paper/2110.02248/) (2021)
- [Online Influence Maximization under the Independent Cascade Model with Node-Level Feedback](https://mlsanity.com/paper/2109.06077/) (2021)
- [Graph Representation Learning for Popularity Prediction Problem: A Survey](https://mlsanity.com/paper/2203.07632/) (2022)
- [Targeted Advertising on Social Networks Using Online Variational Tensor Regression](https://mlsanity.com/paper/2208.10627/) (2022)
- [Social-Inverse: Inverse Decision-making of Social Contagion Management with Task Migrations](https://mlsanity.com/paper/2209.10493/) (2022)
- [Finding Influencers in Complex Networks: An Effective Deep Reinforcement Learning Approach](https://mlsanity.com/paper/2309.07153/) (2023)
- [DSCom: A Data-Driven Self-Adaptive Community-Based Framework for Influence Maximization in Social Networks](https://mlsanity.com/paper/2311.11080/) (2023)
- [MIM-Reasoner: Learning with Theoretical Guarantees for Multiplex Influence Maximization](https://mlsanity.com/paper/2402.16898/) (2024)
- [Proportional Selection in Networks](https://mlsanity.com/paper/2502.03545/) (2025)
- [DQ4FairIM: Fairness-aware Influence Maximization using Deep Reinforcement Learning](https://mlsanity.com/paper/2512.00545/) (2025)
- [Influence Estimation and Maximization via Neural Mean-Field Dynamics](https://mlsanity.com/paper/2106.02608/) (2021)
- [DeHIN: A Decentralized Framework for Embedding Large-scale Heterogeneous Information Networks](https://mlsanity.com/paper/2201.02757/) (2022)
- [Understanding Influence Maximization via Higher-Order Decomposition](https://mlsanity.com/paper/2207.07833/) (2022)
- [Opinion Leader Detection in Online Social Networks Based on Output and Input Links](https://mlsanity.com/paper/2208.13161/) (2022)
- [Jointly Complementary&Competitive Influence Maximization with Concurrent Ally-Boosting and Rival-Preventing](https://mlsanity.com/paper/2302.09620/) (2023)
- [XFlow: Benchmarking Flow Behaviors over Graphs](https://mlsanity.com/paper/2308.03819/) (2023)
- [DySuse: Susceptibility Estimation in Dynamic Social Networks](https://mlsanity.com/paper/2308.10442/) (2023)
- [Pack and Measure: An Effective Approach for Influence Propagation in Social Networks](https://mlsanity.com/paper/2401.00525/) (2023)
- [A Benchmark Study of Deep-RL Methods for Maximum Coverage Problems over Graphs](https://mlsanity.com/paper/2406.14697/) (2024)
- [Online Two-Stage Submodular Maximization](https://mlsanity.com/paper/2510.19480/) (2025)
- [Budgeted Online Influence Maximization](https://mlsanity.com/paper/2604.19672/) (2026)

## Abstract (arXiv)

Given a social network G and a constant k, the influence maximization problem asks for k nodes in G that (directly and indirectly) influence the largest number of nodes under a pre-defined diffusion model. This problem finds important applications in viral marketing, and has been extensively studied in the literature. Existing algorithms for influence maximization, however, either trade approximation guarantees for practical efficiency, or vice versa. In particular, among the algorithms that achieve constant factor approximations under the prominent independent cascade (IC) model or linear threshold (LT) model, none can handle a million-node graph without incurring prohibitive overheads. This paper presents TIM, an algorithm that aims to bridge the theory and practice in influence maximization. On the theory side, we show that TIM runs in O((k+ℓ) (n+m) log n / ε2) expected time and returns a (1-1/e-ε)-approximate solution with at least 1 - n-ℓ probability. The time complexity of TIM is near-optimal under the IC model, as it is only a log n factor larger than the Omega(m + n) lower-bound established in previous work (for fixed k, ℓ, and ε). Moreover, TIM supports the triggering model, which is a general diffusion model that includes both IC and LT as special cases. On the practice side, TIM incorporates novel heuristics that significantly improve its empirical efficiency without compromising its asymptotic performance. We experimentally evaluate TIM with the largest datasets ever tested in the literature, and show that it outperforms the state-of-the-art solutions (with approximation guarantees) by up to four orders of magnitude in terms of running time. In particular, when k = 50, ε = 0.2, and ℓ = 1, TIM requires less than one hour on a commodity machine to process a network with 41.6 million nodes and 1.4 billion edges.