The Densest Subgraph Problem requires us to find, in a given graph, a subset of vertices
whose induced subgraph maximizes a measure of density. The problem has received a …

This paper investigates ultrafilters in the context of connectivity systems, defined as pairs (X,
f) where X is a finite set and f is a symmetric submodular function. Ultrafilters, essential in …

Parameterized complexity/multivariate complexity algorithmics is an exciting field of modern
algorithm design and analysis, with a broad range of theoretical and practical aspects that …

Inspired by a width invariant defined on permutations by Guillemot and Marx [SODA'14], we
introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes …

We define new graph parameters, called flip-width, that generalize treewidth, degeneracy,
and generalized coloring numbers for sparse graphs, and clique-width and twin-width for …

In this survey, we review practical algorithms for graph-theoretic problems that are
expressible in monadic second-order logic. Monadic second-order (MSO) logic allows …

It is known that a number of natural graph problems which are FPT parameterized by
treewidth become W-hard when parameterized by clique-width. It is therefore desirable to …

The aim of this article is to motivate and describe the parameter ecology program, which
studies how different parameters contribute to the difficulty of classical problems. We call for …

Recently, hardness results for problems in P were achieved using reasonable complexity-
theoretic assumptions such as the Strong Exponential Time Hypothesis. According to these …

Many fundamental NP NP-hard problems can be formulated as integer linear programs
(ILPs). A famous algorithm by Lenstra solves ILPs in time that is exponential only in the …