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HSMVS: heuristic search for minimum vertex separator on massive graphs.

Chuan Luo1, Shanyu Guo1

  • 1School of Software, Beihang University, Beijing, China.

Peerj. Computer Science
|June 10, 2024
PubMed
Summary

We developed HSMVS, a new heuristic search algorithm for the minimum vertex separator (MVS) problem on large graphs. HSMVS significantly outperforms existing methods in finding smaller vertex separators for complex graph structures.

Keywords:
Heuristic searchMinimum vertex separator (MVS)Vertex-selection heuristic

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Area of Science:

  • Graph Theory
  • Computational Complexity
  • Algorithm Design

Background:

  • The minimum vertex separator (MVS) problem is a fundamental NP-hard problem in graph theory.
  • Real-world massive graphs necessitate efficient approximate methods, particularly heuristic search algorithms, due to their large scale.

Purpose of the Study:

  • To introduce HSMVS, a novel heuristic search algorithm designed for solving the MVS problem on massive real-world graphs.
  • To demonstrate the effectiveness and efficiency of the proposed HSMVS algorithm.

Main Methods:

  • Developed HSMVS based on an efficient construction procedure.
  • Incorporated a simple yet effective vertex-selection heuristic within the HSMVS algorithm.

Main Results:

  • HSMVS was tested on numerous large-scale, real-world graphs.
  • Experimental results show HSMVS finds significantly smaller vertex separators compared to three established heuristic search algorithms.

Conclusions:

  • The HSMVS algorithm is highly effective for finding minimum vertex separators in massive graphs.
  • The underlying components of HSMVS contribute to its superior performance in practical applications.