Parameterization and approximation are two popular ways of coping with NP-hard
problems. More recently, the two have also been combined to derive many interesting …

We study the complexity of the classic capacitated k-median and k-means problems
parameterized by the number of centers, k. These problems are notoriously difficult since the …

Clustering with capacity constraints is a fundamental problem that attracted significant
attention throughout the years. In this paper, we give the first FPT constant-factor …

The Small Set Expansion Hypothesis is a conjecture which roughly states that it is NP-hard
to distinguish between a graph with a small subset of vertices whose (edge) expansion is …

In Maximum $ k $-Vertex Cover (Max $ k $-VC), the input is an edge-weighted graph $ G $
and an integer $ k $, and the goal is to find a subset $ S $ of $ k $ vertices that maximizes …

In the Min k-Cut problem, the input consists of an edge weighted graph G and an integer k,
and the task is to partition the vertex set into k nonempty sets, such that the total weight of the …

In the k-cut problem, we are given an edge-weighted graph G and an integer k, and have to
remove a set of edges with minimum total weight so that G has at least k connected …

Over the past decade, many results have focused on the design of parameterized
approximation algorithms for W [1]-hard problems. However, there are fundamental …

Submodular maximization under matroid and cardinality constraints are classical problems
with a wide range of applications in machine learning, auction theory, and combinatorial …

Capacitated k-median is one of the few outstanding optimization problems for which the
existence of a polynomial time constant factor approximation algorithm remains an open …