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

Pranabendu Misra, Saket Saurabh, Roohani Sharma, Meirav Zehavi

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)2065-2086
Number of pages22
JournalAlgorithmica
Volume85
Issue number7
DOIs
StatePublished - 1 Jul 2023

Keywords

  • Bounded independence number digraph
  • Directed cutwidth
  • Directed feedback arc set
  • Optimal linear arrangement
  • Sub-exponential fixed-parameter tractable algorithms

ASJC Scopus subject areas

  • Applied Mathematics
  • General Computer Science
  • Computer Science Applications

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