Computational Complexity of Feedback Set and Subset Feedback Set Problems: A Survey

Bai Tian; Xiao Mingyu

doi:10.7544/issn1000-1239.202330693

Journal of Computer Research and Development > 2025 > 62(1): 104-118. > DOI: 10.7544/issn1000-1239.202330693 CSTR: 32373.14.issn1000-1239.202330693

Bai Tian, Xiao Mingyu. Computational Complexity of Feedback Set and Subset Feedback Set Problems: A Survey[J]. Journal of Computer Research and Development, 2025, 62(1): 104-118. DOI: 10.7544/issn1000-1239.202330693

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Computational Complexity of Feedback Set and Subset Feedback Set Problems: A Survey

Bai Tian,
Xiao Mingyu^,

School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731

Funds: This work was supported by the National Natural Science Foundation of China (62372095, 61972070).

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Author Bio:
Bai Tian: born in 1993. PhD. Student member of CCF. His main research interests include graph algorithms and computational complexity

Xiao Mingyu: born in 1979. PhD, professor. Distinguished member of CCF. His main research interests include graph theory and graph algorithms, exact and parameterized algorithms, combinatorial optimization, and mechanism design and algorithmic game theory
Received Date: August 22, 2023
Revised Date: January 21, 2024
Available Online: October 17, 2024

Graphical Abstract

Abstract

Abstract

The feedback set problem is one of the most widely and deeply studied NP-complete graph problems in the field of computer science, with important applications in concurrent computing, large-scale integrated circuits, coding design, software verification, and social network analysis. The subset feedback set problem is a nature generalization of the feedback set problem, and has much universal and practical. In recent several years, the classification of the computational complexity for these two problems has drawn certain interests, and many breakthroughs have been made in the area of algorithms. In this paper, the survey on these problems mainly contains two parts. The first part introduces different versions of the feedback set and subset feedback set problems. The essential relations among these versions and their computational complexity in general graphs are also discussed in this part. The second part introduces the computational complexity of the feedback set and subset feedback set problems in some important and classical graph subclasses, including degree bounded graphs, planar graphs, tournaments, intersection graphs, forbidden graphs, and bipartite graphs. Finally, by analyzing and summarizing the existing research, the major research trends on the feedback set and subset feedback set problems are outlined.
- feedback set problem,
- subset feedback set problem,
- graph theory,
- computational complexity,
- graph algorithms

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References (82)

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