Fixed-Parameter Tractability.- Reductions and Parameterized Intractability.- The Class W[P].- Logic and Complexity.- Two Fundamental Hierarchies.- The First Level of the Hierarchies.- The… Expand

In recent years, graph neural networks (GNNs) have emerged as a powerful neural architecture to learn vector representations of nodes and graphs in a supervised, end-to-end fashion.Expand

We give a complexity theoretic classification of homomorphism problems for graphs and, more generally, relational structures obtained by restricting the left hand side structure in a homomorphism.… Expand

We address the questions of how to estimate the size of a sequence of joins and how to execute the sequence best from a theoretical point of view.Expand

We show that for each property φ of structures that is definable in first-order logic and for each locally tree-decomposable class C of structures, there is an algorithm solving the same problem in time O(n1+(1/k)) (where n is the cardinality of the input structure).Expand

We develop a compression technique for skeletons, based on sharing of common subtrees, which allows us to represent the skeletons of large XML documents in main memory.Expand

A number of efficient methods for evaluating first-order and monadic-second order queries on finite relational structures are based on tree-decompositions of structures or queries.Expand

We develop a parameterized complexity theory for counting problems. As the basis of this theory, we introduce a hierarchy of parameterized counting complexity classes #W$[t]$, for $t\ge 1$, that… Expand

We give a complexity theoretic classification of the counting versions of so-called H-colouring problems for graphs H that may have multiple edges between the same pair of vertices.Expand