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Efficient Partition-based Approaches for Diversified Top-k Subgraph Matching

Liuyi Chen, Yuchen Hu, Zhengyi Yang, Xu Zhou, Wenjie Zhang, Kenli Li

TL;DR

The paper tackles DT$k$SM, the problem of selecting $k$ isomorphic subgraph matches that maximize pairwise topological distances in a data graph. It introduces the Partition-based Distance Diversity (PDD) framework, which partitions the graph, computes inter-partition distances via a Partition Adjacency Graph (PAG), and selects dispersed partitions to drive diverse matching, with parallel HySM and optional inter-partition completion. Two optimizations—embedding-driven partition filtering and densest-based partition selection over a Partition Distance Graph (PDG)—drive efficiency and global dispersion, with theoretical and empirical support. Experiments on 12 datasets show substantial speedups (up to four orders of magnitude) and strong diversity performance (about 95% of cases near 80% of optimal distance diversity and full coverage diversity), indicating practical impact for scalable, globally diverse subgraph matching in domains such as biology, finance, and social networks.

Abstract

Subgraph matching is a core task in graph analytics, widely used in domains such as biology, finance, and social networks. Existing top-k diversified methods typically focus on maximizing vertex coverage, but often return results in the same region, limiting topological diversity. We propose the Distance-Diversified Top-k Subgraph Matching (DTkSM) problem, which selects k isomorphic matches with maximal pairwise topological distances to better capture global graph structure. To address its computational challenges, we introduce the Partition-based Distance Diversity (PDD) framework, which partitions the graph and retrieves diverse matches from distant regions. To enhance efficiency, we develop two optimizations: embedding-driven partition filtering and densest-based partition selection over a Partition Adjacency Graph. Experiments on 12 real world datasets show our approach achieves up to four orders of magnitude speedup over baselines, with 95% of results reaching 80% of optimal distance diversity and 100% coverage diversity.

Efficient Partition-based Approaches for Diversified Top-k Subgraph Matching

TL;DR

The paper tackles DTSM, the problem of selecting isomorphic subgraph matches that maximize pairwise topological distances in a data graph. It introduces the Partition-based Distance Diversity (PDD) framework, which partitions the graph, computes inter-partition distances via a Partition Adjacency Graph (PAG), and selects dispersed partitions to drive diverse matching, with parallel HySM and optional inter-partition completion. Two optimizations—embedding-driven partition filtering and densest-based partition selection over a Partition Distance Graph (PDG)—drive efficiency and global dispersion, with theoretical and empirical support. Experiments on 12 datasets show substantial speedups (up to four orders of magnitude) and strong diversity performance (about 95% of cases near 80% of optimal distance diversity and full coverage diversity), indicating practical impact for scalable, globally diverse subgraph matching in domains such as biology, finance, and social networks.

Abstract

Subgraph matching is a core task in graph analytics, widely used in domains such as biology, finance, and social networks. Existing top-k diversified methods typically focus on maximizing vertex coverage, but often return results in the same region, limiting topological diversity. We propose the Distance-Diversified Top-k Subgraph Matching (DTkSM) problem, which selects k isomorphic matches with maximal pairwise topological distances to better capture global graph structure. To address its computational challenges, we introduce the Partition-based Distance Diversity (PDD) framework, which partitions the graph and retrieves diverse matches from distant regions. To enhance efficiency, we develop two optimizations: embedding-driven partition filtering and densest-based partition selection over a Partition Adjacency Graph. Experiments on 12 real world datasets show our approach achieves up to four orders of magnitude speedup over baselines, with 95% of results reaching 80% of optimal distance diversity and 100% coverage diversity.

Paper Structure

This paper contains 20 sections, 9 theorems, 5 equations, 19 figures, 3 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. PRELIMINARIES
  3. Key Concepts
  4. Problem Statement
  5. The Proposed Method
  6. Overview Framework
  7. Partition-based Graph Preprocessing
  8. Distance-aware Partition Selection
  9. Hybrid Subgraph Matching
  10. Optimizations
  11. Embedding-driven Partition Filtering
  12. Densest-based Partition Selection
  13. Experiments
  14. Initial Partition Evaluation
  15. Efficiency Evaluation
  16. ...and 5 more sections

Key Result

Theorem 1

Finding the top-$k$ subgraph matches that maximize distance-based diversity is NP-Hard, even when all subgraph matches are pre-computed.

Figures (19)

  • Figure 1: Example of Top-$3$ diversified subgraph matches.
  • Figure 2: Example of calculating subgraph distance.
  • Figure 3: Overview Framework
  • Figure 4: Illustration of Partitions Coarsen
  • Figure 5: Neural Partition Filtering: Select $k$ likelihood Partitions(k=2).
  • ...and 14 more figures

Theorems & Definitions (33)

  • Example 1
  • Definition 1: Shortest Path
  • Definition 2: Subgraph Isomorphism
  • Definition 3: Subgraph Matching
  • Definition 4: Diversified Top-$k$ Subgraph matching
  • Definition 5: Coverage-based Diversity 73
  • Definition 6: Subgraph Distance
  • Definition 7: Distance-based Diversity
  • Example 2
  • Remark 1
  • ...and 23 more