Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Decentralized Privacy Preservation for Critical Connections in Graphs

Conggai Li, Wei Ni, Ming Ding, Youyang Qu, Jianjun Chen, David Smith, Wenjie Zhang, Thierry Rakotoarivelo

TL;DR

This work tackles the privacy challenge of releasing subgraph-count queries in graphs while protecting the most sensitive connections of individual vertices. It introduces a fortress-like $p$-cohesion framework to identify a vertex's critical connections via an expand–shrink procedure that yields the minimal $p$-cohesion $MC_p(v,G)$ containing the vertex. The authors then apply a two-phase decentralized differential privacy (DDP) mechanism that perturbs only the intra-$MC_p$ counts ( Phase-1 estimates local sensitivity and Phase-2 adds Laplace noise ), ensuring $(\varepsilon,\delta)$-DDP for the overall query release. Empirical results on nine real-world graphs show that the proposed approach achieves higher data utility than ELV-based methods, by producing denser and smaller critical connection sets and by effectively balancing privacy-utility trade-offs in $k$-clique counting tasks.

Abstract

Many real-world interconnections among entities can be characterized as graphs. Collecting local graph information with balanced privacy and data utility has garnered notable interest recently. This paper delves into the problem of identifying and protecting critical information of entity connections for individual participants in a graph based on cohesive subgraph searches. This problem has not been addressed in the literature. To address the problem, we propose to extract the critical connections of a queried vertex using a fortress-like cohesive subgraph model known as $p$-cohesion. A user's connections within a fortress are obfuscated when being released, to protect critical information about the user. Novel merit and penalty score functions are designed to measure each participant's critical connections in the minimal $p$-cohesion, facilitating effective identification of the connections. We further propose to preserve the privacy of a vertex enquired by only protecting its critical connections when responding to queries raised by data collectors. We prove that, under the decentralized differential privacy (DDP) mechanism, one's response satisfies $(\varepsilon, δ)$-DDP when its critical connections are protected while the rest remains unperturbed. The effectiveness of our proposed method is demonstrated through extensive experiments on real-life graph datasets.

Decentralized Privacy Preservation for Critical Connections in Graphs

TL;DR

This work tackles the privacy challenge of releasing subgraph-count queries in graphs while protecting the most sensitive connections of individual vertices. It introduces a fortress-like -cohesion framework to identify a vertex's critical connections via an expand–shrink procedure that yields the minimal -cohesion containing the vertex. The authors then apply a two-phase decentralized differential privacy (DDP) mechanism that perturbs only the intra- counts ( Phase-1 estimates local sensitivity and Phase-2 adds Laplace noise ), ensuring -DDP for the overall query release. Empirical results on nine real-world graphs show that the proposed approach achieves higher data utility than ELV-based methods, by producing denser and smaller critical connection sets and by effectively balancing privacy-utility trade-offs in -clique counting tasks.

Abstract

Many real-world interconnections among entities can be characterized as graphs. Collecting local graph information with balanced privacy and data utility has garnered notable interest recently. This paper delves into the problem of identifying and protecting critical information of entity connections for individual participants in a graph based on cohesive subgraph searches. This problem has not been addressed in the literature. To address the problem, we propose to extract the critical connections of a queried vertex using a fortress-like cohesive subgraph model known as -cohesion. A user's connections within a fortress are obfuscated when being released, to protect critical information about the user. Novel merit and penalty score functions are designed to measure each participant's critical connections in the minimal -cohesion, facilitating effective identification of the connections. We further propose to preserve the privacy of a vertex enquired by only protecting its critical connections when responding to queries raised by data collectors. We prove that, under the decentralized differential privacy (DDP) mechanism, one's response satisfies -DDP when its critical connections are protected while the rest remains unperturbed. The effectiveness of our proposed method is demonstrated through extensive experiments on real-life graph datasets.
Paper Structure (20 sections, 2 theorems, 21 equations, 11 figures, 2 tables, 3 algorithms)

This paper contains 20 sections, 2 theorems, 21 equations, 11 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Problem and Approach Overview
  4. Overview of Our Approach
  5. Critical Connection Identification
  6. Expand Procedure
  7. Shrink Procedure
  8. Differentially Private Query Release Over Critical Connections
  9. Qualification of DDP on Critical Connections
  10. Differentially Private Query Release
  11. Evaluation
  12. Experimental Setting
  13. Statistical Evaluation for Minimal $p$-Cohesions
  14. Minimal $p$-Cohesions with Different Score Functions
  15. Minimal $p$-Cohesion v.s. Extended Loccal View
  16. ...and 5 more sections

Key Result

Theorem 1

Given a graph $G$, a vertex $v_i$, its minimal $p$-cohesion $MC_p(v_i)$, and a noise scale $\lambda$, we can assert that $\Gamma_{S}^*(v_i) = \Gamma_{S_{in}}(v_i) + Lap(\lambda) + \Gamma_{S_{out}}(v_i)$ ensures $\frac{LS(\Gamma_{S_{in}})}{\lambda}$-DDP, where $LS(\Gamma_{S_{in}})$ is the maximum loc

Figures (11)

  • Figure 1: Motivating Example
  • Figure 2: Density Distribution of Minimal $p$-Cohesions under Different Score Functions
  • Figure 3: Size Distribution of Minimal $p$-Cohesions under Different Score Functions
  • Figure 4: Density Distribution of Minimal $p$-Cohesion and ELV
  • Figure 5: Size Distribution of Minimal $p$-Cohesion and ELV
  • ...and 6 more figures

Theorems & Definitions (11)

  • Example 1
  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Example 2
  • Theorem 1
  • proof
  • Theorem 2
  • ...and 1 more