On the hardness of inclusion-wise minimal separators enumeration - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2023

On the hardness of inclusion-wise minimal separators enumeration


Enumeration problems are often encountered as key subroutines in the exact computation of graph parameters such as chromatic number, treewidth, or treedepth. In the case of treedepth computation, the enumeration of inclusion-wise minimal separators plays a crucial role. However and quite surprisingly, the complexity status of this problem has not been settled since it has been posed as an open direction by Kloks and Kratsch in 1998. Recently at the PACE 2020 competition dedicated to treedepth computation, solvers have been circumventing that by listing all minimal $a$-$b$ separators and filtering out those that are not inclusion-wise minimal, at the cost of efficiency. Naturally, having an efficient algorithm for listing inclusion-wise minimal separators would drastically improve such practical algorithms. In this note, however, we show that no efficient algorithm is to be expected from an output-sensitive perspective, namely, we prove that there is no output-polynomial time algorithm for inclusion-wise minimal separators enumeration unless P = NP.
Fichier principal
Vignette du fichier
2308.15444.pdf (563.42 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-04216381 , version 1 (13-03-2024)



Caroline Brosse, Oscar Defrain, Kazuhiro Kurita, Vincent Limouzy, Takeaki Uno, et al.. On the hardness of inclusion-wise minimal separators enumeration. 2023. ⟨hal-04216381⟩
52 View
7 Download



Gmail Facebook X LinkedIn More