Contraction Bidimensionality of Geometric Intersection Graphs

Given a graph G , we define bcg ( G ) as the minimum k for which G can be contracted to the uniformly triangulated grid Γ k . A graph class G has the SQG C property if every graph G ∈ G has treewidth O ( bcg ( G ) c ) for some 1 ≤ c < 2 . The SQG C property is important for algorithm design as it...

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Veröffentlicht in:Algorithmica Jg. 84; H. 2; S. 510 - 531
Hauptverfasser: Baste, Julien, Thilikos, Dimitrios M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.02.2022
Springer Nature B.V
Springer Verlag
Schlagworte:
Algorithm Analysis and Problem Complexity
Algorithms
Combinatorial analysis
Computational Complexity
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Algorithms
Data Structures and Information Theory
Discrete Mathematics
Graphs
Mathematics of Computing
Theory of Computation
Bidimensionality
Parameterized algorithms
Treewidth
Grid exlusion theorem
String Graphs
Geometric intersection graphs
ISSN:0178-4617, 1432-0541
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Zusammenfassung:Given a graph G , we define bcg ( G ) as the minimum k for which G can be contracted to the uniformly triangulated grid Γ k . A graph class G has the SQG C property if every graph G ∈ G has treewidth O ( bcg ( G ) c ) for some 1 ≤ c < 2 . The SQG C property is important for algorithm design as it defines the applicability horizon of a series of meta-algorithmic results, in the framework of bidimensionality theory, related to fast parameterized algorithms, kernelization, and approximation schemes. These results apply to a wide family of problems, namely problems that are contraction-bidimensional . Our main combinatorial result reveals a wide family of graph classes that satisfy the SQG C property. This family includes, in particular, bounded-degree string graphs. This considerably extends the applicability of bidimensionality theory for contraction bidimensional problems.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-021-00912-w