Vertex k-center problem introduces the notion to recognize k locations as centers in a given network of n connected nodes holding the condition of triangle inequality. This paper presents an efficient algorithm that provides a better solution for vertex k-center problem. Anticipatory Bound Selection Procedure (ABSP) is deployed to find the initial threshold distance (or radius) and eradicating ...

We present an O(n log n) time algorithm for the (weighted) k-center problem of n points on a real line. We show that the problem has an Ω(n log n) time lower bound, and thus our algorithm is optimal. We also show that the problem is solvable in O(n) time in certain special cases. Our techniques involve developing efficient data structures for processing queries that find a lowest point in the c...

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...

Given a metric graph G = (V,E,w) and a positive integer k, the Single Allocation k-Hub Center problem is to find a spanning subgraph H of G such that (i) C ⊂ V is a clique of size k in H; (ii) V \ C forms an independent set in H; (iii) each v ∈ V \C is adjacent to exactly one vertex in C; and (iv) the diameter D(H) is minimized. The vertices selected in C are called hubs and the rest of vertice...

The standard k-center clustering problem is very sensitive to outliers. Charikar et al. proposed an alternative algorithm to cluster p points out of n total, thereby avoiding the distortion caused by outliers. The algorithm has an approximation bound of three times the true solution, but is very slow if implemented naively. We propose a modified implementation of the algorithm that runs signifi...