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...

Clustering is an important problem and has numerous applications. In this paper we consider an important clustering problem, called the k-center problem. We are given a discrete point set S and a constant integer k, and the goal is to compute a set of k center points to minimize the maximum distance from any point of S to its closest center. We consider both the discrete formulation, in which c...

We study the computational aspects of the single-assignment p-hub center problem on the basis of a basic model and a new model. The new model's performance is substantially better in CPU time than di€erent linearizations of the basic model. We also prove the NP-Hardness of the problem. Ó 2000 Elsevier Science B.V. All rights reserved.

The geodesic k-center problem in a simple polygon with n vertices consists in the following. Find a set S of k points in the polygon that minimizes the maximum geodesic distance from any point of the polygon to its closest point in S. In this paper, we focus on the case where k = 2 and present an exact algorithm that returns a geodesic 2-center in O(n log n) time.

In this paper, we observe that bandwidth sharing via TCP in commodity data center networks organized in multi-rooted tree topologies can lead to severe unfairness, which we term as the TCP Outcast problem, under many common traffic patterns. When many flows and a few flows arrive at two ports of a switch destined to one common output port, the small set of flows lose out on their throughput sha...

We present two improved algorithms for weighted discrete p-center problem for tree networks with n vertices. One of our proposed algorithms runs in O(n logn + p log n log(n/p)) time. For all values of p, our algorithm thus runs as fast as or faster than the most efficient O(n log n) time algorithm obtained by applying Cole’s speed-up technique [10] to the algorithm due to Megiddo and Tamir [20]...

S-systems are simple examples of power-law dynamical systems (polynomial systems with real exponents). For planar S-systems, we study global stability of the unique positive equilibrium and solve the center problem. Further, we construct a planar S-system with two limit cycles.

Given a set V of n points and the distances between each pair, the k-center problem asks us to choose a subset C V of size k that minimizes the maximum over all points of the distance from C to the point. This problem is NPhard even when the distances are symmetric and satisfy the triangle inequality, and Hochbaum and Shmoys gave a best-possible 2-approximation for this case. We consider the ve...

We develop a simple and practical exact algorithm for the problem of locating p facilities and assigning clients to them within capacity restrictions in order to minimize the maximum distance between a client and the facility to which it is assigned (capacitated p-center). The algorithm iteratively sets a maximum distance value within which it tries to assign all clients, and thus solves bin-pa...

The p-center problem is one of choosing p facilities from a set of candidates to satisfy the demands of n clients in order to minimize the maximum cost between a client and the facility to which it is assigned. In this article, PBS, a population based meta-heuristic for the p-center problem, is described. PBS is a genetic algorithm based meta-heuristic that uses phenotype crossover and directed...