Domination and Cut Problems on Chordal Graphs with Bounded Leafage

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 201...

Full description

Saved in:
Bibliographic Details
Published in:Algorithmica Vol. 86; no. 5; pp. 1428 - 1474
Main Authors: Galby, Esther, Marx, Dániel, Schepper, Philipp, Sharma, Roohani, Tale, Prafullkumar
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2024
Springer Nature B.V
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Chordal graphs
Computer Science
Computer Sciences
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Datavetenskap (datalogi)
Dominating set
FPT algorithms
Graphs
Leafage
Mathematics of Computing
MultiCut with undeletable terminals
Multiway cut with undeletable terminals
Parameterization
Theory of Computation
Leafage
MultiCut with undeletable terminals
Multiway cut with undeletable terminals
Dominating set
Chordal graphs
FPT algorithms
ISSN:0178-4617, 1432-0541, 1432-0541
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 2 O ( ℓ 2 ) · n O ( 1 ) . We present a conceptually much simpler algorithm that runs in time 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 W[1]-hard when parameterized by the leafage and complement this result by presenting a simple 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 O ( 1 ) -time.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0178-4617
1432-0541
1432-0541
DOI:10.1007/s00453-023-01196-y