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 any ...

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...

The clustering problem of big data in the era artificial intelligence has been widely studied. Because huge amount data, distributed algorithms are often used to deal with problems. computing model an attractive feature: it can handle massive datasets that cannot be put into main memory. On other hand, since many decisions made automatically by machines today's society, algorithm fairness is al...

We consider the k-center problem, in which the centers are constrained to lie on two axis-parallel lines. Given a set of n weighted points in the plane, which are sorted according to their x-coordinates, we show how to test in O(n logn) time if k piercing points placed on two lines, parallel to the x-axis, can pierce all the disks of different radii centered at the n given points. This leads to...

In this work, we study an extension of the k-center facility location problem, where centers are required to service a minimum of clients. This problem is motivated by requirements to balance the workload of centerswhile allowing each center to cater to a spread of clients.We study three variants of this problem, all of which are shown to beNP-hard. In-approximation hardness and approximation a...

In this paper, we consider the k-center problem for streaming points in Rd. More precisely, we consider the single-pass streaming model, where each point in the stream is allowed to be examined only once and a small amount of information can be stored in a device. Since the size of memory is much smaller than the size of the data in the streaming model, it is important to develop an algorithm w...

In this paper, we consider a coverage problem for uncertain points in a tree. Let T be a tree containing a set P of n (weighted) demand points, and the location of each demand point Pi ∈ P is uncertain but is known to appear in one of mi points on T each associated with a probability. Given a covering range λ, the problem is to find a minimum number of points (called centers) on T to build faci...

Optimization of facility location problem is one of the prominent areas of research since last few decades. The vertex k-center problem represents a common occurring problem with in public and private sectors. Consistent efforts are going towards optimal solution of this NP-hard nature problem. The aim of this paper is to highlight the different aspects of algorithmic approach made in this area...

This paper explores three concepts: the k-center problem, some of its variants, and asymmetry. The k-center problem is a fundamental clustering problem, similar to the k-median problem. Variants of k-center may more accurately model real-life problems than the original formulation. Asymmetry is a significant impediment to approximation in many graph problems, such as k-center, facility location...