On the Parameterized Complexity of Graph Modification to First-Order Logic Properties

Fedor V. Fomin (1) , Petr A. Golovach (1) , Dimitrios M. Thilikos (2)

1 UiB - Department of Informatics [Bergen]
2 ALGCO - Algorithmes, Graphes et Combinatoire

We establish connections between parameterized/kernelization complexity of graph modification problems and expressibility in logic. For a first-order logic formula $\varphi$, we consider the problem of deciding whether an input graph can be modified by removing/adding at most $k$ vertices/edges such that the resulting modification has the property expressible by $\varphi$. We provide sufficient and necessary conditions on the structure of the prefix of $\varphi$ specifying when the corresponding graph modification problem is fixed-parameter tractable (parameterized by $k$) and when it admits a polynomial kernel.

Mots clés: First-order logic; Graph modification; Parameterized complexity; Descriptive complexity; Kernelization

Domaines: Complexité [cs.CC]; Combinatoire [math.CO]; Logique en informatique [cs.LO]; Algorithme et structure de données [cs.DS]

Fedor V. Fomin, Petr A. Golovach, Dimitrios M. Thilikos. On the Parameterized Complexity of Graph Modification to First-Order Logic Properties. Theory of Computing Systems, 2020, 64 (2), pp.251-271. ⟨10.1007/s00224-019-09938-8⟩. ⟨hal-03002648⟩