The goal of this textbook is twofold. First, the book serves as an introduction to the field of
parameterized algorithms and complexity accessible to graduate students and advanced …

The survey is a comprehensive overview of the developing area of parameterized
algorithms for graph modification problems. It describes state of the art in kernelization …

Given an undirected graph G, a collection (s1, t1),...,(sl, tl) of pairs of vertices, and an integer
p, the Edge Multicut problem ask if there is a set S of at most p edges such that the removal …

We present a new deterministic algorithm for the Feedback Vertex Set problem
parameterized by the solution size. Our algorithm runs in O⁎((2+ ϕ) k) time, where ϕ< 1.619 …

We introduce a new technique for designing fixed-parameter algorithms for cut problems,
called randomized contractions. We apply our framework to obtain the first fixed-parameter …

A directed odd cycle transversal of a directed graph (digraph) D is a vertex set S that
intersects every odd directed cycle of D. In the Directed Odd Cycle Transversal (DOCT) …

Given a directed graph G, a set of k terminals, and an integer p, the Directed Vertex Multiway
Cut problem asks whether there is a set S of at most p (nonterminal) vertices whose removal …

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

We show a flow-augmentation algorithm in directed graphs: There exists a randomized
polynomial-time algorithm that, given a directed graph G, two integers s, t∈ V (G), and an …

In the Subset Feedback Vertex Set (Subset FVS) problem, the input is a graph G on n
vertices and m edges, a subset of vertices T, referred to as terminals, and an integer k. The …