The k-center problem with triangle inequality is that of placing k center nodes in a weighted undirected graph in which the edge weights obey the triangle inequality, so that the maximum distance of any node to its nearest center is minimized. In this paper, we consider a generalization of this problem where, given a number p, we wish to place k centers so as to minimize the maximum distance of...

For a set P of n points in R, the Euclidean 2-center problem computes a pair of congruent disks of the minimal radius that cover P . We extend this to the (2, k)-center problem where we compute the minimal radius pair of congruent disks to cover n − k points of P . We present a randomized algorithm with O(nk log n) expected running time for the (2, k)-center problem. We also study the (p, k)-ce...

The basic 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. This problem is known to be NP-hard, and several optimal approximation algorithms that achieve a factor of 2 have been developed for it. We ...

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...

The uniform capacitated vertex k -center problem is an \(\mathcal {NP} \) -hard combinatorial optimization that models real situations where centers can only attend a maximum number of customers, and the travel time or distance from customers to their assigned center has be minimized. This paper introduces polynomial-time constructive heuristic algorithm exploits relationship between this minim...

Abstract We study the k -Center problem, where input is a graph $$G=(V,E)$$ G = ( V , E ) with positive edge weights and an integer , goal to select center vertices $$C \subseteq V$$ <m...

We present a polynomial time heuristic algorithm for the minimum dominating set problem. The algorithm can readily be used for solving the minimum α-all-neighbor dominating set problem and the minimum set cover problem. We apply the algorithm in heuristic solving the minimum k-center problem in polynomial time. Using a standard set of 40 test problems we experimentally show that our k-center al...

an extended star is a tree which has only one vertex with degree larger than two. the -center problem in a graph  asks to find a subset  of the vertices of  of cardinality  such that the maximum weighted distances from  to all vertices is minimized. in this paper we consider the -center problem on the unweighted extended stars, and present some properties to find solution.

The k-center problem is a canonical and long-studied facility location and clustering problem with many applications in both its symmetric and asymmetric forms. Both versions of the problem have tight approximation factors on worst case instances: a 2-approximation for symmetric kcenter and an O(log*(k))-approximation for the asymmetric version. Therefore to improve on these ratios, one must go...