We are given a set of sites $$S=\{ s_1, s_2, \cdots, s_n\}$$ in

We are given a set of sites $$S=\{ s_1, s_2, \cdots, s_n\}$$ in the plane, and we want to choose a set of $$k$$ centers $$C=\{ c_1, c_2, \cdots, c_k\}$$ so that the maximum distance from a site to the nearest center is minimized. Here $$c_i$$ can be an arbitrary point in the plane. A local search algorithm arbitrarily choose $$k$$ points in the plane to be the centers, then - (1) divide $$S$$ into $$k$$ sets, where $$S_i$$ is the set of all sites for which $$c_i$$ is the nearest center; and - (2) for each $$S_i$$, compute the central position as a new center for all the sites in $$S_i$$. If steps (1) and (2) cause the covering radius to strictly decrease, we perform another iteration, otherwise the algorithm stops. When the above local search algorithm terminates, the covering radius of its solution is at most 2 times the optimal covering radius. ~@[](4)

答案：FALSE