The Capacitated K - Center Problem 1
نویسندگان
چکیده
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 algorithms for two di erent versions of this problem that achieve approximation factors of 5 and 6. We also study some generalizations of this problem.
منابع مشابه
Exact and Approximation Algorithms for Clustering (Extended Abstract)
In this paper we present an n O(k 1?1=d) time algorithm for solving the k-center problem in R d , under L1 and L2 met-rics. The algorithm extends to other metrics, and to the discrete k-center problem. We also describe a simple (1+)-approximation algorithm for the k-center problem, with running time O(n log k) + (k==) O(k 1?1=d). Finally, we present a n O(k 1?1=d) time algorithm for solving the...
متن کاملExact and Approximation Algortihms for Clustering
In this paper we present a n O(k 1 1=d ) time algorithm for solving the k-center problem in R d , under L 1 and L 2 metrics. The algorithm extends to other metrics, and can be used to solve the discrete k-center problem, as well. We also describe a simple (1 + )-approximation algorithm for the k-center problem, with running time O(n log k) + (k= ) O(k 1 1=d ) . Finally, we present a n O(k 1 1=d...
متن کاملCapacitated k-Center Problem with Vertex Weights
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...
متن کاملThe Heterogeneous Capacitated k-Center Problem
In this paper we initiate the study of the heterogeneous capacitated k-center problem: given a metric space X = (F ∪C, d), and a collection of capacities. The goal is to open each capacity at a unique facility location in F , and also to assign clients to facilities so that the number of clients assigned to any facility is at most the capacity installed; the objective is then to minimize the ma...
متن کاملAn Improved Algorithm for the Hard Uniform Capacitated k-median Problem
In the k-median problem, given a set of locations, the goal is to select a subset of at most k centers so as to minimize the total cost of connecting each location to its nearest center. We study the uniform hard capacitated version of the k-median problem, in which each selected center can only serve a limited number of locations. Inspired by the algorithm of Charikar, Guha, Tardos and Shmoys,...
متن کامل