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Domination and cut problems on chordal graphs with bounded leafage
Citation Link: https://doi.org/10.15480/882.9101
Publikationstyp
Journal Article
Date Issued
2024-05
Sprache
English
TORE-DOI
Journal
Volume
86
Issue
5
Start Page
1428
End Page
1474
Citation
Algorithmica 86 (5): 1428-1474 (2023)
Publisher DOI
Scopus ID
Publisher
Springer
The leafage of a chordal graph G is the minimum integer ℓ such that G can be realized as an intersection graph of subtrees of a tree with ℓ leaves. We consider structural parameterization by the leafage of classical domination and cut problems on chordal graphs. Fomin, Golovach, and Raymond [ESA 2018, Algorithmica 2020] proved, among other things, that Dominating Set on chordal graphs admits an algorithm running in time 2O(ℓ2)·nO(1) . We present a conceptually much simpler algorithm that runs in time 2 O(ℓ)· nO(1) . We extend our approach to obtain similar results for Connected Dominating Set and Steiner Tree. We then consider the two classical cut problems MultiCut with Undeletable Terminals and Multiway Cut with Undeletable Terminals. We prove that the former is W[1]-hard when parameterized by the leafage and complement this result by presenting a simple nO(ℓ) -time algorithm. To our surprise, we find that Multiway Cut with Undeletable Terminals on chordal graphs can be solved, in contrast, in nO(1) -time.
Subjects
Chordal graphs
Dominating set
FPT algorithms
Leafage
MultiCut with undeletable terminals
Multiway cut with undeletable terminals
DDC Class
004: Computer Sciences
Publication version
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