Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Parallel Higher-order Truss Decomposition

Chen Chen, Jingya Qian, Hui Luo, Yongye Li, Xiaoyang Wang

TL;DR

The first research to study the problem of parallel higher-order truss decomposition is conducted, and a parallel framework is first proposed to accelerate the processing.

Abstract

The k-truss model is one of the most important models in cohesive subgraph analysis. The k-truss decomposition problem is to compute the trussness of each edge in a given graph, and has been extensively studied. However, the conventional k-truss model is difficult to characterize the fine-grained hierarchical structures in networks due to the neglect of high order information. To overcome the limitation, the higher-order truss model is proposed in the literature. However, the previous solutions only consider non-parallel scenarios. To fill the gap, in this paper, we conduct the first research to study the problem of parallel higher-order truss decomposition. Specifically, a parallel framework is first proposed. Moreover, several optimizations are further developed to accelerate the processing. Finally, experiments over 6 real-world networks are conducted to verify the performance of proposed methods.

Parallel Higher-order Truss Decomposition

TL;DR

The first research to study the problem of parallel higher-order truss decomposition is conducted, and a parallel framework is first proposed to accelerate the processing.

Abstract

The k-truss model is one of the most important models in cohesive subgraph analysis. The k-truss decomposition problem is to compute the trussness of each edge in a given graph, and has been extensively studied. However, the conventional k-truss model is difficult to characterize the fine-grained hierarchical structures in networks due to the neglect of high order information. To overcome the limitation, the higher-order truss model is proposed in the literature. However, the previous solutions only consider non-parallel scenarios. To fill the gap, in this paper, we conduct the first research to study the problem of parallel higher-order truss decomposition. Specifically, a parallel framework is first proposed. Moreover, several optimizations are further developed to accelerate the processing. Finally, experiments over 6 real-world networks are conducted to verify the performance of proposed methods.

Paper Structure

This paper contains 12 sections, 6 theorems, 6 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Baseline Approach
  4. Our Solution
  5. Convergence and Asynchrony in Higher-order Neighborhoods
  6. Parallel Algorithm
  7. Optimizations
  8. Experiments
  9. Experiment setup
  10. Evaluation Results
  11. Related work
  12. Conclusion

Key Result

Lemma 1

Given a graph $G$, a distance threshold $h$ and a positive integer $k$, a $(k+1,h)$-truss of $G$ is a subgraph of $(k,h)$-truss.

Figures (6)

  • Figure 1: Motivation example of higher-order truss decomposition
  • Figure 2: Initial 2-support for all edges
  • Figure 3: Example of parallel iterative process
  • Figure 4: Efficiency evaluation on all the datasets
  • Figure 5: Evaluation of parallel framework
  • ...and 1 more figures

Theorems & Definitions (15)

  • Example 1
  • Definition 1: $k$-truss
  • Definition 2: common $h$-neighbor
  • Definition 3: $h$-support
  • Definition 4: $(k,h)$-truss
  • Lemma 1
  • Example 2
  • Definition 5: triangle edge pair
  • Lemma 2
  • Definition 6: $h$-hop reachable path key
  • ...and 5 more