We present approximation algorithms for the Fault-tolerant $ k $-Supplier with Outliers
($\mathsf {F} k\mathsf {SO} $) problem. This is a common generalization of two known …

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 …

We study the graph burning problem and give a polynomial-time approximation scheme
(PTAS) for arbitrary graphs of constant treewidth. This significantly extends the previous …

In the Non-Uniform $ k $-Center problem, a generalization of the famous $ k $-center
clustering problem, we want to cover the given set of points in a metric space by finding a …

Graph Burning models information spreading in a given graph as a process such that in
each step one node is infected (informed) and also the infection spreads to all neighbors of …

Clustering is a fundamental unsupervised learning method and classic facility location
problem where given a set of items along with pair-wise distances, the goal is to group the …

In this thesis we present and analyze approximation algorithms for three different clustering
problems. The formulations of these problems are motivated by fairness and explainability …