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Dynamic thresholding search for the feedback vertex set problem.

Wen Sun1, Jin-Kao Hao2, Zihao Wu1

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Summary
This summary is machine-generated.

This study introduces a new algorithm for the NP-hard feedback vertex set problem. The iterated dynamic thresholding search algorithm achieves state-of-the-art results on benchmark graphs, finding optimal solutions for most instances.

Keywords:
Descent searchDynamic thresholding searchFeedback vertex setHeuristic

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Area of Science:

  • Computer Science
  • Graph Theory
  • Combinatorial Optimization

Background:

  • The feedback vertex set problem aims to find a minimum vertex subset whose removal makes a directed graph acyclic.
  • This problem is computationally challenging due to its NP-hard nature, limiting practical applications.
  • Existing algorithms struggle to find optimal solutions efficiently for large or complex graphs.

Purpose of the Study:

  • To develop an efficient algorithm for solving the NP-hard feedback vertex set problem.
  • To improve upon the performance of existing state-of-the-art algorithms for this problem.
  • To analyze the impact of key algorithmic components on performance.

Main Methods:

  • Development of an iterated dynamic thresholding search algorithm.
  • Integration of local optimization, dynamic thresholding search, and perturbation techniques.
  • Extensive computational experiments on 101 benchmark directed graphs from diverse sources.

Main Results:

  • The proposed algorithm achieved record-breaking best solutions for 24 graphs.
  • It matched the best-known solutions for 75 out of 101 benchmark graphs.
  • The algorithm demonstrated superior performance compared to current state-of-the-art methods.

Conclusions:

  • The iterated dynamic thresholding search algorithm is highly effective for the feedback vertex set problem.
  • The algorithm offers a significant advancement in solving this computationally challenging problem.
  • Further analysis confirmed the effectiveness of its core components in achieving optimal results.