[Paper Review] Algorithmic Design for Competitive Influence Maximization Problems

Yishi Lin, John C. S. Lui|arXiv (Cornell University)|Oct 31, 2014

Optimization and Search Problems5 references3 citations

TL;DR

This paper proposes TCIM, a general algorithmic framework for Competitive Influence Maximization (CIM) under a novel General Competitive Independent Cascade (GCIC) model. It achieves a (1−1/e−ε)-approximation with high probability and runs up to four orders of magnitude faster than prior state-of-the-art greedy algorithms, making it the first practical framework with both strong theoretical guarantees and efficient performance across diverse influence propagation models.

ABSTRACT

Given the popularity of the viral marketing campaign in online social networks, finding an effective method to identify a set of most influential nodes so to compete well with other viral marketing competitors is of upmost importance. We propose a "General Competitive Independent Cascade (GCIC)" model to describe the general influence propagation of two competing sources in the same network. We formulate the "Competitive Influence Maximization (CIM)" problem as follows: Under a prespecified influence propagation model and that the competitor's seed set is known, how to find a seed set of $k$ nodes so as to trigger the largest influence cascade? We propose a general algorithmic framework TCIM for the CIM problem under the GCIC model. TCIM returns a $(1-1/e-ε)$-approximate solution with probability at least $1-n^{-\ell}$, and has an efficient time complexity of $O(c(k+\ell)(m+n)\log n/ε^2)$, where $c$ depends on specific propagation model and may also depend on $k$ and underlying network $G$. To the best of our knowledge, this is the first general algorithmic framework that has both $(1-1/e-ε)$ performance guarantee and practical efficiency. We conduct extensive experiments on real-world datasets under three specific influence propagation models, and show the efficiency and accuracy of our framework. In particular, we achieve up to four orders of magnitude speedup as compared to the previous state-of-the-art algorithms with the approximate guarantee.

Motivation & Objective

• To address the lack of efficient algorithms with strong approximation guarantees for the Competitive Influence Maximization (CIM) problem in viral marketing scenarios.
• To formalize a general influence propagation model—General Competitive Independent Cascade (GCIC)—that captures diverse competitive dynamics in social networks.
• To design a unified algorithmic framework, TCIM, that guarantees high-quality solutions with practical runtime efficiency across multiple influence propagation models.
• To empirically validate TCIM’s efficiency and effectiveness on real-world datasets under three distinct influence propagation models.

Proposed method

• Propose the General Competitive Independent Cascade (GCIC) model to generalize influence propagation dynamics between two competing sources in a network.
• Formulate the Competitive Influence Maximization (CIM) problem as selecting k seed nodes to maximize influence spread, given a known competitor seed set.
• Design the Two-phase Competitive Influence Maximization (TCIM) framework, which uses randomized RAPG (Reverse Active Path Graph) sampling to estimate influence and select seeds efficiently.
• Integrate a two-phase approach: first, estimate the lower bound of optimal influence using RAPG sampling; second, select k nodes with high marginal gain using the estimated bounds.
• Leverage concentration inequalities and probabilistic analysis to ensure a (1−1/e−ε)-approximation with probability at least 1−n−ℓ.
• Tune the number of RAPG samples based on ε, ℓ, and network size to balance accuracy and efficiency, with complexity scaling as O(c(ℓ+k)(m+n)log n/ε²).

Experimental results

Research questions

• RQ1 Can a general algorithmic framework be designed for Competitive Influence Maximization (CIM) that maintains a (1−1/e−ε)-approximation guarantee across diverse influence propagation models?
• RQ2 How can the computational efficiency of such a framework be improved to make it practical for large-scale networks?
• RQ3 What is the impact of different influence propagation models (e.g., Campaign-Oblivious, Distance-based, Wave) on the performance and complexity of the TCIM framework?
• RQ4 To what extent does TCIM outperform existing greedy algorithms with approximation guarantees in terms of runtime while maintaining solution quality?

Key findings

• TCIM achieves a (1−1/e−ε)-approximation with probability at least 1−n−ℓ, providing strong theoretical performance guarantees.
• For k=50, ε=0.1, and ℓ=1, TCIM returns solutions comparable to state-of-the-art greedy algorithms but runs up to four orders of magnitude faster on large networks like NetHEPT (75,879 nodes, 508,837 edges).
• On the NetHEPT dataset, TCIM completes within 7 seconds when ε=0.5, and within 6 minutes for ε=0.1, demonstrating high scalability.
• The running time of TCIM decreases with increasing ε, consistent with its O(1/ε²) complexity dependence, enabling faster execution with looser approximation bounds.
• Memory consumption varies by model: lowest for Campaign-Oblivious, moderate for Distance-based, and highest for Wave propagation, due to differences in RAPG instance storage requirements.
• As k increases, the number of required RAPG instances decreases, leading to reduced running time and memory usage, especially when the lower bound LB_r increases faster than λ.