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STEPHAN KREUTZER COMPLEXITY OF MODEL-CHECKING PROBLEMS 37/81<br />
INTRODUCTION COMPLEXITY UPPER BOUNDS COMPOSITION LOCALITY LOCALISATION GRIDS GRID-LIKE MINORS LABELLED WEBS<br />
Let Q be the set of red vertices.<br />
Algorithm: Second Step<br />
Second Step: Greedy Approach<br />
L := ∅<br />
Assume m = 4<br />
while Q ≠ ∅ do<br />
choose v ∈ Q<br />
L := L∪{v}<br />
Q := Q \ N 2r (v)<br />
od<br />
if |L| ≥ m then accept<br />
else<br />
all red vertices are within a 2r-neighbourhood of an element of L<br />
if G [ N 2r (L) ] |= ∃x 1 ...x m ( ∧ i≠j dist(x i, x j ) > 2r ∧ ∧ i “x i is red” )<br />
accept else reject<br />
Running time: O(n)