Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

CEMR: An Effective Subgraph Matching Algorithm with Redundant Extension Elimination

Linglin Yang, Xunbin Su, Lei Zou, Xiangyang Gou, Yinnian Lin

TL;DR

A novel subgraph matching algorithm that incorporates two techniques to reduce duplicate extensions: common extension merging, which leverages a black-white vertex encoding, and common extension reusing, which employs common extension buffers.

Abstract

Subgraph matching is a fundamental problem in graph analysis with a wide range of applications. However, due to its inherent NP-hardness, enumerating subgraph matches efficiently on large real-world graphs remains highly challenging. Most existing works adopt a depth-first search (DFS) backtracking strategy, where a partial embedding is gradually extended in a DFS manner along a branch of the search trees until either a full embedding is found or no further extension is possible. A major limitation of this paradigm is the significant amount of duplicate computation that occurs during enumeration, which increases the overall runtime. To overcome this limitation, we propose a novel subgraph matching algorithm, CEMR. It incorporates two techniques to reduce duplicate extensions: common extension merging, which leverages a black-white vertex encoding, and common extension reusing, which employs common extension buffers. In addition, we design two pruning techniques to discard unpromising search branches. Extensive experiments on real-world datasets and diverse query workloads demonstrate that CEMR outperforms state-of-the-art subgraph matching methods.

CEMR: An Effective Subgraph Matching Algorithm with Redundant Extension Elimination

TL;DR

A novel subgraph matching algorithm that incorporates two techniques to reduce duplicate extensions: common extension merging, which leverages a black-white vertex encoding, and common extension reusing, which employs common extension buffers.

Abstract

Subgraph matching is a fundamental problem in graph analysis with a wide range of applications. However, due to its inherent NP-hardness, enumerating subgraph matches efficiently on large real-world graphs remains highly challenging. Most existing works adopt a depth-first search (DFS) backtracking strategy, where a partial embedding is gradually extended in a DFS manner along a branch of the search trees until either a full embedding is found or no further extension is possible. A major limitation of this paradigm is the significant amount of duplicate computation that occurs during enumeration, which increases the overall runtime. To overcome this limitation, we propose a novel subgraph matching algorithm, CEMR. It incorporates two techniques to reduce duplicate extensions: common extension merging, which leverages a black-white vertex encoding, and common extension reusing, which employs common extension buffers. In addition, we design two pruning techniques to discard unpromising search branches. Extensive experiments on real-world datasets and diverse query workloads demonstrate that CEMR outperforms state-of-the-art subgraph matching methods.
Paper Structure (45 sections, 3 theorems, 4 equations, 11 figures, 4 tables, 3 algorithms)

This paper contains 45 sections, 3 theorems, 4 equations, 11 figures, 4 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Motivation
  3. Our Solution
  4. Preliminary and Related Works
  5. Problem Definition
  6. Background and Related Work
  7. Preprocessing Phase
  8. Enumeration Phase
  9. Related Works of Preprocessing Phase
  10. Related Works of Enumeration Phase
  11. Theoretical Foundation
  12. Common Extension Merging
  13. Black-white Vertex Encoding & Aggregated Embedding
  14. Four Cases of Extension
  15. Dealing with Vertex Conflicts
  16. ...and 30 more sections

Key Result

Lemma 1

Given a query graph $Q$ and a matching order $O = (u_0, u_1, \dots, u_{n-1})$, let $M_1$ and $M_2$ be matches of the subquery $Q_i$ induced by the first $i$ vertices. Assume that $M_1$ and $M_2$ share the same mappings for all backward neighbors of $u_i$ (i.e., $N_-^O(u_i)$), and let $v$ be a data v

Figures (11)

  • Figure 1: Subgraph Matching
  • Figure 2: Illustrations of Case 1 and Case 2.
  • Figure 3: Illustrations of Case 3.
  • Figure 4: Illustration of Case 4.
  • Figure 5: The reference set and parent vertex of $u_4$
  • ...and 6 more figures

Theorems & Definitions (19)

  • Example 1
  • definition 1: Subgraph Isomorphism
  • definition 2: Subgraph Matching Problem
  • definition 3: Matching Order
  • definition 4: Backward (Forward) Neighbors
  • Example 2
  • Lemma 1
  • definition 5: Black-White Vertex Encoding & Aggregated Embedding
  • Example 3
  • Example 4
  • ...and 9 more