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Link Recommendation to Augment Influence Diffusion with Provable Guarantees

Xiaolong Chen, Yifan Song, Jing Tang

TL;DR

This paper proposes an algorithm, namely AIS, consisting of an efficient estimator for augmented influence estimation and an accelerated sampling approach that is the first algorithm that can be implemented on large graphs containing millions of nodes while preserving strong theoretical guarantees.

Abstract

Link recommendation systems in online social networks (OSNs), such as Facebook's ``People You May Know'', Twitter's ``Who to Follow'', and Instagram's ``Suggested Accounts'', facilitate the formation of new connections among users. This paper addresses the challenge of link recommendation for the purpose of social influence maximization. In particular, given a graph $G$ and the seed set $S$, our objective is to select $k$ edges that connect seed nodes and ordinary nodes to optimize the influence dissemination of the seed set. This problem, referred to as influence maximization with augmentation (IMA), has been proven to be NP-hard. In this paper, we propose an algorithm, namely \textsf{AIS}, consisting of an efficient estimator for augmented influence estimation and an accelerated sampling approach. \textsf{AIS} provides a $(1-1/\mathrm{e}-\varepsilon)$-approximate solution with a high probability of $1-δ$, and runs in $O(k^2 (m+n) \log (n / δ) / \varepsilon^2 + k \left|E_{\mathcal{C}}\right|)$ time assuming that the influence of any singleton node is smaller than that of the seed set. To the best of our knowledge, this is the first algorithm that can be implemented on large graphs containing millions of nodes while preserving strong theoretical guarantees. We conduct extensive experiments to demonstrate the effectiveness and efficiency of our proposed algorithm.

Link Recommendation to Augment Influence Diffusion with Provable Guarantees

TL;DR

This paper proposes an algorithm, namely AIS, consisting of an efficient estimator for augmented influence estimation and an accelerated sampling approach that is the first algorithm that can be implemented on large graphs containing millions of nodes while preserving strong theoretical guarantees.

Abstract

Link recommendation systems in online social networks (OSNs), such as Facebook's ``People You May Know'', Twitter's ``Who to Follow'', and Instagram's ``Suggested Accounts'', facilitate the formation of new connections among users. This paper addresses the challenge of link recommendation for the purpose of social influence maximization. In particular, given a graph and the seed set , our objective is to select edges that connect seed nodes and ordinary nodes to optimize the influence dissemination of the seed set. This problem, referred to as influence maximization with augmentation (IMA), has been proven to be NP-hard. In this paper, we propose an algorithm, namely \textsf{AIS}, consisting of an efficient estimator for augmented influence estimation and an accelerated sampling approach. \textsf{AIS} provides a -approximate solution with a high probability of , and runs in time assuming that the influence of any singleton node is smaller than that of the seed set. To the best of our knowledge, this is the first algorithm that can be implemented on large graphs containing millions of nodes while preserving strong theoretical guarantees. We conduct extensive experiments to demonstrate the effectiveness and efficiency of our proposed algorithm.
Paper Structure (23 sections, 4 theorems, 8 equations, 7 figures, 3 tables, 2 algorithms)

This paper contains 23 sections, 4 theorems, 8 equations, 7 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Influence Maximization
  4. Diffusion-Aware Link Manipulation
  5. Preliminaries
  6. Problem Definition
  7. Greedy Framework
  8. Reverse Influence Sampling
  9. An Efficient Approximation Algorithm for IMA
  10. An Efficient Estimator via RR Sets
  11. Accelerating RR Sets Generation
  12. Putting It Together
  13. Theoretical Analysis
  14. Analysis of AIS
  15. Comparison with MC-Greedy
  16. ...and 8 more sections

Key Result

Lemma 3.2

Let $A^* = \mathop{\mathrm{arg\,max}}\limits_{\left| A \right|\leq k} f(A)$ be the set maximizing $f(A)$ among all sets with size at most $k$, where $f$ is monotone and submodular, and $f(\emptyset) = 0$. For any $\varepsilon > 0$ and any $0< \lambda \leq \frac{\varepsilon / k}{2 + \varepsilon / k}$

Figures (7)

  • Figure 1: Results on GRQC and NetHEPT ($\varepsilon=0.5$).
  • Figure 2: Running time on GRQC and NetHEPT
  • Figure 3: Expected spread with varying $k$ ($\varepsilon=0.5$).
  • Figure 4: Running time with varying $k$ ($\varepsilon=0.5$).
  • Figure 5: Results with varying $\varepsilon$.
  • ...and 2 more figures

Theorems & Definitions (5)

  • Definition 3.1: IMA d2019recommending
  • Lemma 3.2: chen2013information
  • Lemma 3.3: borgs2014maximizing
  • Lemma 4.1
  • Theorem 5.1