Robust k-Center with Two Types of Radii

02/23/2021
by   Deeparnab Chakrabarty, et al.
0

In the non-uniform k-center problem, the objective is to cover points in a metric space with specified number of balls of different radii. Chakrabarty, Goyal, and Krishnaswamy [ICALP 2016, Trans. on Algs. 2020] (CGK, henceforth) give a constant factor approximation when there are two types of radii. In this paper, we give a constant factor approximation for the two radii case in the presence of outliers. To achieve this, we need to bypass the technical barrier of bad integrality gaps in the CGK approach. We do so using "the ellipsoid method inside the ellipsoid method": use an outer layer of the ellipsoid method to reduce to stylized instances and use an inner layer of the ellipsoid method to solve these specialized instances. This idea is of independent interest and could be applicable to other problems. Keywords: Approximation, Clustering, Outliers, and Round-or-Cut.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/06/2021

Towards Non-Uniform k-Center with Constant Types of Radii

In the Non-Uniform k-Center problem we need to cover a finite metric spa...
research
11/11/2021

Non-Uniform k-Center and Greedy Clustering

In the Non-Uniform k-Center problem, a generalization of the famous k-ce...
research
02/26/2018

Improved MapReduce and Streaming Algorithms for k-Center Clustering (with Outliers)

We present efficient MapReduce and Streaming algorithms for the k-center...
research
06/30/2022

Approximation Algorithms for Continuous Clustering and Facility Location Problems

We consider the approximability of center-based clustering problems wher...
research
02/28/2021

Is Simple Uniform Sampling Efficient for Center-Based Clustering With Outliers: When and Why?

Clustering has many important applications in computer science, but real...
research
04/20/2020

A Sub-linear Time Framework for Geometric Optimization with Outliers in High Dimensions

Many real-world problems can be formulated as geometric optimization pro...
research
11/07/2022

A Simple Combinatorial Algorithm for Robust Matroid Center

Recent progress on robust clustering led to constant-factor approximatio...

Please sign up or login with your details

Forgot password? Click here to reset