Before revision:  Our algorithm modifies the guard placement locally while ensuring the updated orthogonal polygon with h holes and n vertices , is guarded using at most \lfloor (n+2h)/4 \rfloor vertex guards.
After revision:  Our algorithm modifies the guard placement in O(k \lg{(n+n') while ensuring the updated orthogonal polygon with h holes and n vertices , is guarded using at most \lfloor (n+2h)/4 \rfloor vertex guards.