Dynamic Complexity Meets Parameterised Algorithms [article]

Jonas Schmidt, Thomas Schwentick, Nils Vortmeier, Thomas Zeume, Ioannis Kokkinis
2019 arXiv   pre-print
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
more » ... his 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.
arXiv:1910.06281v2 fatcat:kqxvs46ed5cblkuj2liutee2m4