Dynamic thresholding search for the feedback vertex set problem

• Published in: PeerJ. Computer science Vol. 9; p. e1245
• Main Authors: Sun, Wen, Hao, Jin-Kao, Wu, Zihao, Li, Wenlong, Wu, Qinghua
• Format: Journal Article
• Language: English
• Published: United States PeerJ. Ltd 10.02.2023; PeerJ, Inc; PeerJ; PeerJ Inc
• Subjects: Algorithms; Algorithms and Analysis of Algorithms; Analysis; Approximation; Computer Science; Descent search; Dynamic thresholding search; Experiments; Feedback; Feedback vertex set; Graph theory; Graphs; Heuristic; Local optimization; Optimization Theory and Computation; Perturbation; Search algorithms; Vertex sets; Dynamic thresholding search; Descent search; Feedback vertex set; Heuristic
• ISSN: 2376-5992; 2376-5992
• DOI: 10.7717/peerj-cs.1245

Given a directed graph G = ( V, E ), a feedback vertex set is a vertex subset C whose removal makes the graph G acyclic. The feedback vertex set problem is to find the subset C * whose cardinality is the minimum. As a general model, this problem has a variety of applications. However, the problem is known to be NP-hard, and thus computationally challenging. To solve this difficult problem, this article develops an iterated dynamic thresholding search algorithm, which features a combination of local optimization, dynamic thresholding search, and perturbation. Computational experiments on 101 benchmark graphs from various sources demonstrate the advantage of the algorithm compared with the state-of-the-art algorithms, by reporting record-breaking best solutions for 24 graphs, equally best results for 75 graphs, and worse best results for only two graphs. We also study how the key components of the algorithm affect its performance of the algorithm.