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Dynamic Complexity Meets Parameterised Algorithms

Authors Jonas Schmidt, Thomas Schwentick, Nils Vortmeier, Thomas Zeume, Ioannis Kokkinis

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Author Details

Jonas Schmidt
  • TU Dortmund University, Dortmund, Germany
Thomas Schwentick
  • TU Dortmund University, Dortmund, Germany
Nils Vortmeier
  • TU Dortmund University, Dortmund, Germany
Thomas Zeume
  • TU Dortmund University, Dortmund, Germany
Ioannis Kokkinis
  • TU Dortmund University, Dortmund, Germany

Funding

The authors acknowledge the financial support by DFG grant SCHW 678/6-2.

Acknowledgements

We are grateful to Till Tantau for some valuable discussions.

Cite AsGet BibTex

Jonas Schmidt, Thomas Schwentick, Nils Vortmeier, Thomas Zeume, and Ioannis Kokkinis. Dynamic Complexity Meets Parameterised Algorithms. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.CSL.2020.36

Abstract

Dynamic Complexity studies the maintainability of queries with logical formulas in a setting where the underlying structure or database changes over time. Most often, these formulas are from first-order logic, giving rise to the dynamic complexity class DynFO. This paper investigates extensions of DynFO in the spirit of parameterised algorithms. In this setting structures come with a parameter k and the extensions allow additional "space" of size f(k) (in the form of an additional structure of this size) or additional time f(k) (in the form of iterations of formulas) or both. The resulting classes are compared with their non-dynamic counterparts and other classes. The main part of the paper explores the applicability of methods for parameterised algorithms to this setting through case studies for various well-known parameterised problems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Logic and databases
  • Theory of computation → Complexity theory and logic
Keywords
  • Dynamic complexity
  • parameterised complexity

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