Before revision:  and, k is the sum of the number of vertices added to or removed from the orthogonal polygon, the number of cuts in the L-shaped partitioning of the free space of the orthogonal polygon that got affected due to the update, and the number of channels affected due to the update. For the special case of the initial orthogonal polygon being hole-free, and each update resulting in a hole-free orthogonal polygon, our dynamic guard updating algorithmtakes O(k\lg{(n+n')) worst-case time.
After revision:  and, k is the sum of the number of vertices added to or removed from the orthogonal polygon, the number of cuts in the L-shaped partitioning of the free space of the orthogonal polygon that got affected due to the update, and the number of ) worst-case time.