For instance, this problem can be used to model the placement of fire stations within a city, in order to ensure that every address within the city can be reached quickly by a fire truck. Gonzalez described a clustering heuristic that selects as centers the first "k" points of a farthest-first traversal, and then assigns each of the input points to its nearest center. If "r" is the distance from the set of "k" selected centers to the next point at position "k" + 1 in the traversal, then this clustering achieves a distance of "r". However, the subset of "k" centers together with the next point are all at distance at least "r" from each other, and any "k"-clustering would put two of these points into one cluster, so there is no clustering with distance better than "r"/2. Thus, Gonzalez's heuristic gives an approximation ratio of 2 for this problem. This heuristic, and the name "farthest-first traversal", are often incorrectly attributed to a different paper from the same time, . However, Hochbaum and Shmoys used graph-theoretic techniques, not the farthest-first traversal, to obtain a different approximation algorithm for the metric "k"-center with the same approximation ratio as Gonzalez's heuristic. For both the min-max diameter clustering problem and the metric "k"-center problem, these approximations are optimal: the existence of a polynomial-time heuristic with any constant approximation ratio less than 2 would imply that P = NP. As well as for clustering, the farthest-first traversal can also be used in another type of facility location problem, the max-min facility dispersion problem, in which the goal is to choose the locations of "k" different facilities so that they are as far apart from each other as possible. More precisely, the goal in this problem is to choose "k" points from a given metric space or a given set of candidate points, in such a way as to maximize the minimum pairwise distance between the selected points. Again, this can be approximated by choosing the first "k" points of a farthest-first traversal. If "r" denotes the distance of the "k"th point from all previous points, then every point of the metric space or the candidate set is within distance "r" of the first "k" − 1 points.