[Paper Review] Tracking Top-K Influential Vertices in Dynamic Networks

Yang Yu, Zhefeng Wang+3 more|arXiv (Cornell University)|Mar 5, 2018

Data Stream Mining Techniques10 references3 citations

TL;DR

This paper proposes a scalable, provably accurate method for tracking the top-k most influential vertices in dynamic networks under the linear threshold (LT) and independent cascade (IC) models. By maintaining a sample of random RR sets and using two O(1)-time signals to dynamically adjust the number of RR sets, the approach ensures multiplicative error guarantees and achieves up to an order of magnitude speedup in influence maximization queries compared to prior work.

ABSTRACT

Influence propagation in networks has enjoyed fruitful applications and has been extensively studied in literature. However, only very limited preliminary studies tackled the challenges in handling highly dynamic changes in real networks. In this paper, we tackle the problem of tracking top-$k$ influential vertices in dynamic networks, where the dynamic changes are modeled as a stream of edge weight updates. Under the popularly adopted linear threshold (LT) model and the independent cascade (IC) model, we address two essential versions of the problem: tracking the top-$k$ influential individuals and finding the best $k$-seed set to maximize the influence spread (Influence Maximization). We adopt the polling-based method and maintain a sample of random RR sets so that we can approximate the influence of vertices with provable quality guarantees. It is known that updating RR sets over dynamic changes of a network can be easily done by a reservoir sampling method, so the key challenge is to efficiently decide how many RR sets are needed to achieve good quality guarantees. We use two simple signals, which both can be accessed in $O(1)$ time, to decide a proper number of RR sets. We prove the effectiveness of our methods. For both tasks the error incurred in our method is only a multiplicative factor to the ground truth. For influence maximization, we also propose an efficient query algorithm for finding the $k$ seeds, which is one order of magnitude faster than the state-of-the-art query algorithm in practice. In addition to the thorough theoretical results, our experimental results on large real networks clearly demonstrate the effectiveness and efficiency of our algorithms.

Motivation & Objective

• To address the challenge of tracking top-k influential vertices in large, highly dynamic networks with real-time edge weight updates.
• To provide provable quality guarantees for influence estimation and seed set selection under the LT and IC models.
• To eliminate the need for prior knowledge of network properties by using relative error thresholds instead of absolute thresholds.
• To design an efficient, scalable algorithm that maintains a minimal number of RR sets while ensuring high accuracy.
• To accelerate influence maximization queries by optimizing the greedy seed selection process on sampled RR sets.

Proposed method

• Uses a polling-based approach with random reverse reachable (RR) sets to approximate vertex influence with provable accuracy.
• Employs reservoir sampling to efficiently update RR sets in response to dynamic edge weight changes.
• Introduces two O(1)-time signals to determine the optimal number of RR sets needed for desired error bounds.
• Applies theoretical bounds on RR set size using the inverse of the influence spread function to ensure multiplicative error guarantees.
• Proposes a novel greedy query algorithm (New Greedy) that accelerates influence maximization by reducing redundant computations.
• Uses a practical heuristic sample size based on theoretical bounds to balance accuracy and efficiency in practice.

Experimental results

Research questions

• RQ1 How can we maintain accurate influence estimates for top-k influential vertices in a dynamic network with continuous edge updates?
• RQ2 What is a lightweight, efficient method to determine the number of RR sets required to achieve a desired relative error in influence estimation?
• RQ3 Can we design a query algorithm for influence maximization that is significantly faster than existing methods while preserving solution quality?
• RQ4 How do the proposed methods scale with large, real-world dynamic networks under both LT and IC influence propagation models?
• RQ5 To what extent can the number of RR sets be reduced without sacrificing accuracy in dynamic influence tracking?

Key findings

• The proposed method ensures that the relative error in influence estimation is bounded by a multiplicative factor of the true influence, even without prior knowledge of the network.
• The algorithm maintains up to 10 times fewer RR sets than the state-of-the-art method of Ohsaka et al. [20], significantly improving space efficiency.
• The New Greedy query algorithm runs up to an order of magnitude faster than the Lazy Evaluation method in [20], achieving results in under 300ms on the Twitter network.
• On the largest dataset (Twitter), the system processed 0.3 billion updates in under 4 hours, demonstrating strong scalability.
• The practical sample size heuristic, based on theoretical bounds, performs effectively in practice, maintaining high accuracy with minimal RR sets.
• The method achieves a relative error rate of at most 2% in influence estimation on real-world networks, as confirmed by empirical evaluation.