given a set  of  points in the plane and a constant ,-center problem is to find two closed disks which each covers the whole , the diameter of the bigger one is minimized, and the distance of the two centers is at least . constrained -center problem is the -center problem in which the centers are forced to lie on a given line . in this paper, we first introduce -center problem and its constrain...

The capacitated K-center problem is a fundamental facility location problem, where we are asked to locate K facilities in a graph, and to assign vertices to facilities, so as to minimize the maximum distance from a vertex to the facility to which it is assigned. Moreover, each facility may be assigned at most L vertices. This problem is known to be NP-hard. We give polynomial time approximation...

Given a set P of n points in R, a typical clustering problem asks for partitioning P into a family of k subsets {P1, . . . , Pk}, so that a certain objective function is minimized. The objective function depends on the application and varies. A typical clustering problem is the so-called centered clustering problem in which a representative point ci (or a q-flat) is chosen for each cluster Pi a...

We study the capacitated k-center problem with vertex weights. It is a generalization of the well known k-center problem. In this variant each vertex has a weight and a capacity. The assignment cost of a vertex to a center is given by the product of the weight of the vertex and its distance to the center. The distances are assumed to form a metric. Each center can only serve as many vertices as...

The capacitated K-center problem is a fundamental facility location problem, where we are asked to locate K facilities in a graph, and to assign vertices to facilities, so as to minimize the maximum distance from a vertex to the facility to which it is assigned. Moreover, each facility may be assigned at most L vertices. This problem is known to be NP-hard. We give polynomial time approximation...

In this paper, we introduce and study the Non-Uniform k-Center (NUkC) problem. Given a finite metric space (X, d) and a collection of balls of radii {r1 ≥ · · · ≥ rk}, the NUkC problem is to find a placement of their centers on the metric space and find the minimum dilation α, such that the union of balls of radius α · ri around the ith center covers all the points in X . This problem naturally...