• Publications
  • Influence
Parameterized Complexity Theory
  • J. Flum, Martin Grohe
  • Mathematics, Computer Science
  • Texts in Theoretical Computer Science. An EATCS…
  • 2006
Fixed-Parameter Tractability.- Reductions and Parameterized Intractability.- The Class W[P].- Logic and Complexity.- Two Fundamental Hierarchies.- The First Level of the Hierarchies.- TheExpand
Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks
TLDR
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
The complexity of homomorphism and constraint satisfaction problems seen from the other side
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
Size Bounds and Query Plans for Relational Joins
TLDR
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
Deciding first-order properties of locally tree-decomposable structures
TLDR
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
Path Queries on Compressed XML
TLDR
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
Query evaluation via tree-decompositions
TLDR
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
The Parameterized Complexity of Counting Problems
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 $t\ge 1$, thatExpand
The complexity of partition functions
TLDR
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
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