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Counting frequent patterns in large labeled graphs: a hypergraph-based approach.

Jinghan Meng1, Napath Pitaksirianan1, Yi-Cheng Tu1

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Data Mining and Knowledge Discovery
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Summary
This summary is machine-generated.

This study introduces a new hypergraph framework to unify graph mining support measures, developing novel minimum instance (MI) and minimum vertex cover (MVC) measures. The research reveals constant-factor approximation algorithms for MVC and maximum independent set (MIS) in polynomial time.

Keywords:
Data miningGraph miningHypergraphSupport measure

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Area of Science:

  • Graph databases and data mining
  • Hypergraph theory and algorithms
  • Computational complexity and approximation algorithms

Background:

  • Graph databases are increasingly popular for information representation.
  • Frequent pattern mining in single graphs faces challenges in support measure and search schemes.
  • Existing support measures, like minimum-image-based and overlap-graph-based, have limitations.

Purpose of the Study:

  • To propose a novel framework for designing support measures in single-graph mining.
  • To introduce new support measures, minimum instance (MI) and minimum vertex cover (MVC), based on occurrence/instance hypergraphs.
  • To unify and analyze existing and new support measures, revealing their bounding relations and hardness properties.

Main Methods:

  • Developed a framework based on occurrence/instance hypergraphs to unify support measures.
  • Introduced and analyzed new support measures: minimum instance (MI) and minimum vertex cover (MVC).
  • Utilized linear programming and semidefinite programming for polynomial-time relaxations of MVC and maximum independent set (MIS).

Main Results:

  • The proposed framework unifies most major existing and new support measures.
  • Minimum instance (MI) measure is shown to be closely related to the number of pattern instances.
  • Constant-factor approximation algorithms for MVC and MIS were discovered, challenging prior assumptions.
  • Polynomial-time relaxations for MVC and MIS were developed, with counts bounded within a constant factor.

Conclusions:

  • The hypergraph-based framework effectively unifies diverse support measures in graph mining.
  • New measures like MI and MVC offer advantages and are well-characterized within the framework.
  • The study provides significant insights into the approximation and complexity of graph mining measures.