Clustering to minimize the maximum intercluster distance

AbstractThe problem of clustering a set of points so as to minimize the maximum intercluster distance is studied. An O(kn) approximation algorithm, where n is the number of points and k is the number of clusters, that guarantees solutions with an objective function value within two times the optimal solution value is presented. This approximation algorithm succeeds as long as the set of points satisfies the triangular inequality. We also show that our approximation algorithm is best possible, with respect to the approximation bound, if P ≠ NP

Estimating Financial Trends by Spline Fitting via Fisher Algoritm

Trends have a crucial role in finance such as setting investment strategies and technical analysis.  Determining trend changes in an optimal way is the main aim of this study. The model of this study improves the optimality by spline fitting to the equations to reduce the error terms. The results show that spline fitting is more efficient compared to line fitting by % and Fisher Method by %. This method may be used to determine regime switches as well

Fault Tolerant Clustering Revisited

In discrete k-center and k-median clustering, we are given a set of points P in a metric space M, and the task is to output a set C \subseteq ? P, |C| = k, such that the cost of clustering P using C is as small as possible. For k-center, the cost is the furthest a point has to travel to its nearest center, whereas for k-median, the cost is the sum of all point to nearest center distances. In the fault-tolerant versions of these problems, we are given an additional parameter 1 ?\leq \ell \leq ? k, such that when computing the cost of clustering, points are assigned to their \ell-th nearest-neighbor in C, instead of their nearest neighbor. We provide constant factor approximation algorithms for these problems that are both conceptually simple and highly practical from an implementation stand-point

Approximation Algorithms for Geometric Median Problems

In this paper we present approximation algorithms for median problems in metric spaces and xed-dimensional Euclidean space. Our algorithms use a new method for transforming an optimal solution of the linear program relaxation of the s-median problem into a provably good integral solution. This transfor- mation technique is fundamentally di erent from the methods of randomized and deterministic rounding [Rag, RaT] and the methods proposed in [LiV] in the following way: Previous techniques never set variables with zero values in the fractional solution to 1. This departure from previous methods is crucial for the success of our algorithms