Domination and Cut Problems on Chordal Graphs with Bounded Leafage
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Published:2023-12-29
Issue:
Volume:
Page:
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ISSN:0178-4617
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Container-title:Algorithmica
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language:en
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Short-container-title:Algorithmica
Author:
Galby Esther,Marx Dániel,Schepper Philipp,Sharma Roohani,Tale Prafullkumar
Abstract
AbstractThe leafage of a chordal graph G is the minimum integer $$\ell $$
ℓ
such that G can be realized as an intersection graph of subtrees of a tree with $$\ell $$
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 $$2^{\mathcal {O}(\ell ^2)} \cdot n^{\mathcal {O}(1)}$$
2
O
(
ℓ
2
)
·
n
O
(
1
)
. We present a conceptually much simpler algorithm that runs in time $$2^{\mathcal {O}(\ell )} \cdot n^{\mathcal {O}(1)}$$
2
O
(
ℓ
)
·
n
O
(
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 [1]-hard when parameterized by the leafage and complement this result by presenting a simple $$n^{\mathcal {O}(\ell )}$$
n
O
(
ℓ
)
-time algorithm. To our surprise, we find that Multiway Cut with Undeletable Terminals on chordal graphs can be solved, in contrast, in $$n^{{{\mathcal {O}}}(1)}$$
n
O
(
1
)
-time.
Funder
Technische Universität Hamburg
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computer Science Applications,General Computer Science
Reference49 articles.
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