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

Soft Constraints of Difference and Equality

no code implementations • 16 Jan 2014 • Emmanuel Hebrard, Dániel Marx, Barry O'Sullivan, Igor Razgon

Moreover, we show that the maximum number of pairs of equal variables can be approximated by a factor 1/2 with a linear time greedy algorithm.