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XMiner: Efficient Directed Subgraph Matching with Pattern Reduction

Pingpeng Yuan, Yujiang Wang, Tianyu Ma, Siyuan He, Ling Liu

TL;DR

Directed graph pattern matching is challenging due to edge directions. The paper introduces XMiner, which builds and reduces a pattern digraph G=(V,E) by discovering constraint inclusion relationships, producing a reduced graph G' and an execution plan that reuses intermediate results. The core contributions include a formalization of constraint inclusion, a heuristic reduction algorithm to obtain a minimum constraint cover S (where S covers all edges), and a plan-driven, parallel matching engine that extends results to removed constraints. Experiments on real datasets show XMiner outperforming state-of-the-art undirected systems on directed patterns, with strong scalability and modest memory usage. This approach broadens practical directed subgraph matching capabilities on large graphs.

Abstract

Graph pattern matching, one of the fundamental graph mining problems, aims to extract structural patterns of interest from an input graph. The state-of-the-art graph matching algorithms and systems are mainly designed for undirected graphs. Directed graph matching is more complex than undirected graph matching because the edge direction must be taken into account before the exploration of each directed edge. Thus, the technologies (e.g. storage, exploiting symmetry for graph matching) for undirected graph matching may not be fully applicable to directed graphs. For example, the redundancy implied in directed graph pattern can not be detected using the symmetry breaking for undirected pattern graph. Here, we present XMiner for efficient directed graph pattern matching whose core idea is 'pattern reduction'. It first analyzes the relationship between constraints implied in a pattern digraph. Then it reduces the pattern graph into a simplified form by finding a minimum constraint cover. Finally, XMiner generates an execution plan and follows it to extract matchings of the pattern graph. So, XMiner works on simplified pattern graph and avoids much data access and redundant computation throughout the matching process. Our experimental results show that XMiner outperforms state-of the-art stand-alone graph matching systems, and scales to complex graph pattern matching tasks on larger graph.

XMiner: Efficient Directed Subgraph Matching with Pattern Reduction

TL;DR

Directed graph pattern matching is challenging due to edge directions. The paper introduces XMiner, which builds and reduces a pattern digraph G=(V,E) by discovering constraint inclusion relationships, producing a reduced graph G' and an execution plan that reuses intermediate results. The core contributions include a formalization of constraint inclusion, a heuristic reduction algorithm to obtain a minimum constraint cover S (where S covers all edges), and a plan-driven, parallel matching engine that extends results to removed constraints. Experiments on real datasets show XMiner outperforming state-of-the-art undirected systems on directed patterns, with strong scalability and modest memory usage. This approach broadens practical directed subgraph matching capabilities on large graphs.

Abstract

Graph pattern matching, one of the fundamental graph mining problems, aims to extract structural patterns of interest from an input graph. The state-of-the-art graph matching algorithms and systems are mainly designed for undirected graphs. Directed graph matching is more complex than undirected graph matching because the edge direction must be taken into account before the exploration of each directed edge. Thus, the technologies (e.g. storage, exploiting symmetry for graph matching) for undirected graph matching may not be fully applicable to directed graphs. For example, the redundancy implied in directed graph pattern can not be detected using the symmetry breaking for undirected pattern graph. Here, we present XMiner for efficient directed graph pattern matching whose core idea is 'pattern reduction'. It first analyzes the relationship between constraints implied in a pattern digraph. Then it reduces the pattern graph into a simplified form by finding a minimum constraint cover. Finally, XMiner generates an execution plan and follows it to extract matchings of the pattern graph. So, XMiner works on simplified pattern graph and avoids much data access and redundant computation throughout the matching process. Our experimental results show that XMiner outperforms state-of the-art stand-alone graph matching systems, and scales to complex graph pattern matching tasks on larger graph.
Paper Structure (21 sections, 2 theorems, 9 figures, 4 tables, 2 algorithms)

This paper contains 21 sections, 2 theorems, 9 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Overview of XMiner
  4. Pattern Graph Reduction
  5. Finding Constraint Inclusion Relationship
  6. Reducing Pattern Graph
  7. Pattern Matching
  8. Plan Generation and Execution
  9. Intermediate Result Reuse
  10. Generating Results
  11. Implementation
  12. Evaluation
  13. Experimental Settings
  14. Performance Comparison
  15. Data Graph
  16. ...and 6 more sections

Key Result

Theorem 2.1

Let $e_1: (u_1,v_1)$, $e_2: (u_2,v_2)$$\in\mathbb{G}$, if $u_1\sqsubseteq u_2$, then $e_1\sqsubseteq e_2$ denoted as $(e_1) ^{u_1}\sqsubseteq (e_2) ^{u_2}$. Similarly, if $v_1\sqsubseteq v_2$, then $e_1\sqsubseteq e_2$, denoted as $(e_1) ^{v_1}\sqsubseteq (e_2) ^{v_2}$.

Figures (9)

  • Figure 1: Data Graph and Example Pattern Graph
  • Figure 2: Reduced Pattern Graphs and Their matching Plans
  • Figure 3: The Example Plan Execution
  • Figure 4: Pattern Graphs
  • Figure 5: XMiner with/without Pattern Reduction
  • ...and 4 more figures

Theorems & Definitions (9)

  • Definition 2.1: Digraph
  • Definition 2.2: Pattern Graph
  • Definition 2.3: Path
  • Definition 2.4: Constraint Inclusion
  • Definition 2.5: Conditional Inclusion
  • Theorem 2.1
  • Theorem 2.2
  • Definition 2.6: Inclusion Set
  • Definition 2.7: Constraint Cover