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 …

Preprocessing, or data reduction, is a standard technique for simplifying and speeding up
computation. Written by a team of experts in the field, this book introduces a rapidly …

We give an algorithm that, given an-vertex graph and an integer, in time either outputs a tree
decomposition of of width at most or determines that the treewidth of is larger than. This is …

We give an algorithm that for an input n-vertex graph G and integer k>0, in time 2^O(k)n,
either outputs that the treewidth of G is larger than k, or gives a tree decomposition of G of …

We give an algorithm that takes as input an n-vertex graph G and an integer k, runs in time 2
O (k 2) n O (1), and outputs a tree decomposition of G of width at most k, if such a …

We investigate the complexity of several fundamental polynomial-time solvable problems on
graphs and on matrices, when the given instance has low treewidth; in the case of matrices …

The Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural
hardness assumption concerning the problem of approximating the edge expansion of small …

We present a data structure that for a dynamic graph G that is updated by edge insertions
and deletions, maintains a tree decomposition of G of width at most 6k+5 under the promise …

We study graph ordering problems with a min-max objective. A classical problem of this type
is cutwidth, where given a graph we want to order its vertices such that the number of edges …

Treewidth is an important graph invariant, relevant for both structural and algorithmic
reasons. A necessary condition for a graph class to have bounded treewidth is the absence …