Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Efficient size-prescribed $k$-core search

Yiping Liu, Bo Yan, Bo Zhao, Hongyi Su, Yang Chen, Michael Witbrock

TL;DR

The TSizeKcore-BU algorithm proves to be highly efficient in finding size-prescribed k-core subgraphs on large datasets, making it a favorable choice for such scenarios, and the TSizeKcore-TD algorithm is better suited for small datasets where running time is less critical.

Abstract

$k$-core is a subgraph where every node has at least $k$ neighbors within the subgraph. The $k$-core subgraphs has been employed in large platforms like Network Repository to comprehend the underlying structures and dynamics of the network. Existing studies have primarily focused on finding $k$-core groups without considering their size, despite the relevance of solution sizes in many real-world scenarios. This paper addresses this gap by introducing the size-prescribed $k$-core search (SPCS) problem, where the goal is to find a subgraph of a specified size that has the highest possible core number. We propose two algorithms, namely the {\it TSizeKcore-BU} and the {\it TSizeKcore-TD}, to identify cohesive subgraphs that satisfy both the $k$-core requirement and the size constraint. Our experimental results demonstrate the superiority of our approach in terms of solution quality and efficiency. The {\it TSizeKcore-BU} algorithm proves to be highly efficient in finding size-prescribed $k$-core subgraphs on large datasets, making it a favorable choice for such scenarios. On the other hand, the {\it TSizeKcore-TD} algorithm is better suited for small datasets where running time is less critical.

Efficient size-prescribed $k$-core search

TL;DR

The TSizeKcore-BU algorithm proves to be highly efficient in finding size-prescribed k-core subgraphs on large datasets, making it a favorable choice for such scenarios, and the TSizeKcore-TD algorithm is better suited for small datasets where running time is less critical.

Abstract

-core is a subgraph where every node has at least neighbors within the subgraph. The -core subgraphs has been employed in large platforms like Network Repository to comprehend the underlying structures and dynamics of the network. Existing studies have primarily focused on finding -core groups without considering their size, despite the relevance of solution sizes in many real-world scenarios. This paper addresses this gap by introducing the size-prescribed -core search (SPCS) problem, where the goal is to find a subgraph of a specified size that has the highest possible core number. We propose two algorithms, namely the {\it TSizeKcore-BU} and the {\it TSizeKcore-TD}, to identify cohesive subgraphs that satisfy both the -core requirement and the size constraint. Our experimental results demonstrate the superiority of our approach in terms of solution quality and efficiency. The {\it TSizeKcore-BU} algorithm proves to be highly efficient in finding size-prescribed -core subgraphs on large datasets, making it a favorable choice for such scenarios. On the other hand, the {\it TSizeKcore-TD} algorithm is better suited for small datasets where running time is less critical.
Paper Structure (8 sections, 1 theorem, 2 figures, 1 table, 4 algorithms)

This paper contains 8 sections, 1 theorem, 2 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related work
  3. The size-prescribed $k$-core search Problem
  4. The TSizeKCore Algorithm
  5. The Top-down strategy
  6. The Bottom-up strategy
  7. Experiments
  8. Summary

Key Result

Theorem 1

The SPCS problem is (a) $W[1]$-hard; (b) hard-to-approximate within $n^{1-\epsilon}$ for any $\epsilon>0$. ∎

Figures (2)

  • Figure 1: Effectiveness. The experiment compares the core number of subgraphs outputted by different algorithms with varying $t$.
  • Figure 2: The average running time of different algorithms. We further list the running time of TSizeKcore-BU on large datasets. The running time of the S-greedy, Critical, and TSizeKcore-TD algorithms is not listed due to their excessive running time.

Theorems & Definitions (1)

  • Theorem 1