On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem

We study the parameterized complexity of the Bounded-Degree Vertex Deletion problem (BDD), where the aim is to find a maximum induced subgraph whose maximum degree is below a given degree bound. Our focus lies on parameters that measure the structural properties of the input instance. We first show...

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Vydané v:Algorithmica Ročník 83; číslo 1; s. 297 - 336
Hlavní autori: Ganian, Robert, Klute, Fabian, Ordyniak, Sebastian
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.01.2021
Springer Nature B.V
Predmet:
Algorithm Analysis and Problem Complexity
Algorithms
Complexity
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Deletion
Feedback
Graph theory
Mathematics of Computing
Parameterization
Parameters
Theory of Computation
Vertex sets
Treecut width
Parameterized algorithms
Feedback vertex set
Bounded-degree vertex deletion
ISSN:0178-4617, 1432-0541
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Popis
Shrnutí:We study the parameterized complexity of the Bounded-Degree Vertex Deletion problem (BDD), where the aim is to find a maximum induced subgraph whose maximum degree is below a given degree bound. Our focus lies on parameters that measure the structural properties of the input instance. We first show that the problem is W[1]-hard parameterized by a wide range of fairly restrictive structural parameters such as the feedback vertex set number, pathwidth, treedepth, and even the size of a minimum vertex deletion set into graphs of pathwidth and treedepth at most three. We thereby resolve an open question stated in Betzler, Bredereck, Niedermeier and Uhlmann (2012) concerning the complexity of BDD parameterized by the feedback vertex set number. On the positive side, we obtain fixed-parameter algorithms for the problem with respect to the decompositional parameter treecut width and a novel problem-specific parameter called the core fracture number.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-020-00758-8