Slides.

STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 45/81
INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS
Localisation of Graph Invariants
Definition:
Let f : GRAPHS → N be a graph invariant.
We define its localisation loc f : GRAPHS×N → N as
{ (
loc f (G, r) := max f G [ N r (v) ]) }
: v ∈ V(G) .
A class C of graphs has bounded local f , if there is a computable function
h : N → N such that loc f (G, r) ≤ h(r) for all G ∈ C and r ∈ N.
Example: f : G ↦→ tw(G) tree-width of graphs
{ (
loc f (G, r) := max tw G [ N r (v) ]) }
: v ∈ V(G)
Bounded local tree-width