Sub-exponential Time Parameterized Algorithms for Graph Layout Problems on Digraphs with Bounded Independence Number

Fradkin and Seymour (J Comb Theory Ser B 110:19–46, 2015) defined the class of digraphs of bounded independence number as a generalization of the class of tournaments. They argued that the class of digraphs of bounded independence number is structured enough to be exploited algorithmically. In this...

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Vydáno v:Algorithmica Ročník 85; číslo 7; s. 2065 - 2086
Hlavní autoři: Misra, Pranabendu, Saurabh, Saket, Sharma, Roohani, Zehavi, Meirav
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.07.2023
Springer Nature B.V
Témata:
Algorithm Analysis and Problem Complexity
Algorithms
Arc cutting
Combinatorial analysis
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Graph theory
Mathematics of Computing
Parameterization
Theory of Computation
05C20
68Q25
68W40
Optimal linear arrangement
Directed feedback arc set
Directed cutwidth
05C85
68R05
97K20
Bounded independence number digraph
97P20
Sub-exponential fixed-parameter tractable algorithms
ISSN:0178-4617, 1432-0541
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Shrnutí:Fradkin and Seymour (J Comb Theory Ser B 110:19–46, 2015) defined the class of digraphs of bounded independence number as a generalization of the class of tournaments. They argued that the class of digraphs of bounded independence number is structured enough to be exploited algorithmically. In this paper, we further strengthen this belief by showing that several cut problems that admit sub-exponential time parameterized algorithms (a trait uncommon to parameterized algorithms) on tournaments, including Directed Feedback Arc Set , Directed Cutwidth and Optimal Linear Arrangement , also admit such algorithms on digraphs of bounded independence number. Towards this, we rely on the generic approach of Fomin and Pilipczuk (in: Proceedings of the Algorithms—ESA 2013—21st Annual European Symposium, Sophia Antipolis, France, September 2–4, 2013, pp. 505–516, 2013), where to get the desired algorithms, it is enough to bound the number of k -cuts in digraphs of bounded independence number by a sub-exponential FPT function (Fomin and Pilipczuk bounded the number of k -cuts in transitive tournaments). Specifically, our main technical contribution is a combinatorial result that proves that the yes-instances of the problems (defined above) have a sub-exponential number of k -cuts. We prove this bound by using a combination of chromatic coding, inductive reasoning and exploiting the structural properties of these digraphs.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-022-01093-w