An Efficient Algorithm for 2D Euclidean 2-Center with Outliers
نویسندگان
چکیده
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)-center problem in R under the `∞-metric for p = {4, 5}. We propose an kn log n algorithm for computing a `∞ (4, k)-center and an kn log n algorithm for computing a `∞ (5, k)-center.
منابع مشابه
Efficient Approximation Algorithms for Point-set Diameter in Higher Dimensions
We study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...
متن کاملAn Efficient Algorithm for Euclidian 2-Center with Outliers∗
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...
متن کاملMinimum Spanning Tree-based Structural Similarity Clustering for Image Mining with Local Region Outliers
Image mining is more than just an extension of data mining to image domain. Image mining is a technique commonly used to extract knowledge directly from image. Image segmentation is the first step in image mining. We treat image segmentation as graph partitioning problem. In this paper we propose a novel algorithm, Minimum Spanning Tree based Structural Similarity Clustering for Image Mining wi...
متن کاملIdentification of outliers types in multivariate time series using genetic algorithm
Multivariate time series data, often, modeled using vector autoregressive moving average (VARMA) model. But presence of outliers can violates the stationary assumption and may lead to wrong modeling, biased estimation of parameters and inaccurate prediction. Thus, detection of these points and how to deal properly with them, especially in relation to modeling and parameter estimation of VARMA m...
متن کاملImproved MapReduce and Streaming Algorithms for k-Center Clustering (with Outliers)
We present efficient MapReduce and Streaming algorithms for the $k$-center problem with and without outliers. Our algorithms exhibit an approximation factor which is arbitrarily close to the best possible, given enough resources.
متن کامل