| Issue |
RAIRO-Theor. Inf. Appl.
Volume 58, 2024
Randomness and Combinatorics - Edited by Luca Ferrari & Paolo Massazza
|
|
|---|---|---|
| Article Number | 18 | |
| Number of page(s) | 16 | |
| DOI | https://doi.org/10.1051/ita/2024015 | |
| Published online | 19 December 2024 | |
Enumerating Minimum Feedback Vertex Sets in directed graphs with union-cat trees
* Corresponding author: abdenbi.moussa@uqam.ca
Received:
15
December
2022
Accepted:
15
October
2024
The problem of finding a minimum feedback vertex set (MFVS) in a directed graph has been known to be NP-hard for around 40 years: It is one of the problems listed in Karp’s famous 1972 paper. Several strategies to solve the MFVS problem, both exact and approximate, have been proposed. In particular, in 2000, Lin and Jou presented an exact algorithm based on eight graph contraction operators whose complexity is polynomial for a particular class of graphs called DOME-contractible graphs. This paper proposes two contributions. First, we introduce a data structure called union-cat tree that provides, in some cases, a compact representation of a family of constant size subsets of a given finite set. Secondly, we extend Lin and Jou’s algorithm to compute the set of all MFVSs of any directed graph.
Mathematics Subject Classification: 05C05 / 05C20 / 05C30
Key words: Directed graphs / Feedback vertex set / Union-cat tree
© The authors. Published by EDP Sciences, 2024
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