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Faster algorithms for counting subgraphs in sparse graphs.

Marco Bressan1

  • 1Dipartimento di Informatica, Università Statale di Milano, Milan, Italy.

Algorithmica
|November 1, 2021
PubMed
Summary
This summary is machine-generated.

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This study introduces a novel tree decomposition for sparse graphs, enabling faster subgraph counting. The new dynamic programming approach significantly improves performance on graphs with bounded degeneracy or average degree.

Area of Science:

  • Graph Theory
  • Algorithms
  • Computational Complexity

Background:

  • The subgraph counting problem involves finding occurrences of a pattern graph (H) within a larger host graph (G).
  • Existing algorithms face challenges with efficiency, particularly when the host graph is sparse.
  • Understanding subgraph counts is crucial in various fields, including network analysis and bioinformatics.

Purpose of the Study:

  • To investigate whether subgraph counting can be accelerated in sparse graphs.
  • To develop a novel algorithmic approach for subgraph counting in directed acyclic graphs (DAGs).
  • To establish new theoretical bounds for subgraph counting complexity in sparse graph settings.

Main Methods:

  • Introduction of a novel tree-like decomposition tailored for directed acyclic graphs.
Keywords:
DegeneracySparsitySubgraph countingTree decomposition

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  • Development of a dynamic programming algorithm that leverages graph degeneracy.
  • Analysis of algorithmic performance based on graph properties like degeneracy and average degree.

    • Main Results:

    • A new method for subgraph counting in sparse graphs that outperforms existing state-of-the-art algorithms.
    • Demonstrated time complexity improvements for counting induced subgraphs in bounded-degeneracy graphs.
    • Established theoretical bounds and lower bounds, characterizing the complexity of subgraph counting in sparse graphs.

    Conclusions:

    • Sparse graphs allow for significantly faster subgraph counting compared to dense graphs.
    • The proposed tree decomposition and dynamic programming approach provide a powerful tool for subgraph counting.
    • The findings offer a comprehensive understanding of subgraph counting complexity in bounded-degeneracy graphs.