Diversity-aware clustering: Computational Complexity and Approximation Algorithms

no code implementations • 10 Jan 2024 • Suhas Thejaswi, Ameet Gadekar, Bruno Ordozgoiti, Aristides Gionis

We present parameterized approximation algorithms with approximation ratios $1+ \frac{2}{e}$, $1+\frac{8}{e}$ and $3$ for diversity-aware $k$-median, diversity-aware $k$-means and diversity-aware $k$-supplier, respectively.

Clustering

Parameterized Approximation for Robust Clustering in Discrete Geometric Spaces

no code implementations • 12 May 2023 • Fateme Abbasi, Sandip Banerjee, Jarosław Byrka, Parinya Chalermsook, Ameet Gadekar, Kamyar Khodamoradi, Dániel Marx, Roohani Sharma, Joachim Spoerhase

Given a constant $z\ge 1$, the input to Robust $(k, z)$-Clustering is a set $P$ of $n$ weighted points in a metric space $(M,\delta)$ and a positive integer $k$.

Clustering Fairness +1

Parameterized Approximation Schemes for Clustering with General Norm Objectives

no code implementations • 6 Apr 2023 • Fateme Abbasi, Sandip Banerjee, Jarosław Byrka, Parinya Chalermsook, Ameet Gadekar, Kamyar Khodamoradi, Dániel Marx, Roohani Sharma, Joachim Spoerhase

Notable results of this kind include EPASes in the high-dimensional Euclidean setting for $k$-center [Bad\u{o}iu, Har-Peled, Indyk; STOC'02] as well as $k$-median, and $k$-means [Kumar, Sabharwal, Sen; J. ACM 2010].

Clustering

On learning k-parities with and without noise

no code implementations • 18 Feb 2015 • Arnab Bhattacharyya, Ameet Gadekar, Ninad Rajgopal

We improve the previous best result of Buhrman et al. by an $\exp(k)$ factor in the time complexity.

Learning Theory