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 …

In the Feedback Vertex Set (FVS) problem, one is given an undirected graph G and an
integer k, and one needs to determine whether there exists a set of k vertices that intersects …

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 …

In the Topological Minor Deletion (TM-Deletion) problem, the input consists of an undirected
graph G, a family of undirected graphs F and an integer k. The task is to determine whether …

Let H be a planar graph. By a classical result of Robertson and Seymour, there is a function
f: ℕ→ ℝ such that for all k∊ ℕ and all graphs G, either G contains k vertex-disjoint subgraphs …

We investigate preprocessing for vertex-subset problems on graphs. While the notion of
kernelization, originating in parameterized complexity theory, is a formalization of provably …

We study efficient preprocessing for the undirected Feedback Vertex Set problem, a
fundamental problem in graph theory which asks for a minimum-sized vertex set whose …

We develop a new framework for generalizing approximation algorithms from the structural
graph algorithm literature so that they apply to graphs somewhat close to that class (a …