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Parameterized Complexity Theory
Fixed-Parameter Tractability.- Reductions and Parameterized Intractability.- The Class W[P].- Logic and Complexity.- Two Fundamental Hierarchies.- The First Level of the Hierarchies.- The…
Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks
It is shown that GNNs have the same expressiveness as the Weisfeiler-Leman graph isomorphism heuristic in terms of distinguishing non-isomorphic (sub-)graphs, and a generalization of GNN's is proposed, so-called $k$-dimensional GNNS ($k-GNNs), which can take higher-order graph structures at multiple scales into account.
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
The complexity of homomorphism and constraint satisfaction problems seen from the other side
- Martin Grohe
- Mathematics44th Annual IEEE Symposium on Foundations of…
- 11 October 2003
It is proved that, under some complexity theoretic assumption from parameterized complexity theory, HOM(C, /spl I.bar/) is in polynomial time if, and only if, the cores of all structures in C have bounded tree-width.
Size Bounds and Query Plans for Relational Joins
- Albert Atserias, Martin Grohe, D. Marx
- Computer Science49th Annual IEEE Symposium on Foundations of…
- 25 October 2008
This work studies relational joins from a theoretical perspective and shows that there exist queries for which the join-project plan suggested by the fractional edge cover approach may be substantially better than any join plan that does not use intermediate projections.
Deciding first-order properties of locally tree-decomposable structures
It is shown 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 a linear time algorithm deciding whether a given structure A ∈ C hasproperty φ.
The parameterized complexity of counting problems
- J. Flum, Martin Grohe
- Computer ScienceThe 43rd Annual IEEE Symposium on Foundations of…
- 16 November 2002
The main result states that counting cycles and paths of length k in both directed and undirected graphs, parameterized by k, are #W-complete, which makes it highly unlikely that any of these problems is fixed-parameter tractable, even though their decision versions are.
Query evaluation via tree-decompositions
It is shown that the acyclic and bounded tree-width fragments have the same expressive power as the well-known guarded fragment and the finite-variable fragments of first-order logic, respectively.
The complexity of first-order and monadic second-order logic revisited
It is shown that unless PTIME=NP, the model-checking problem for monadic second-order logic on finite words is not solvable in time f(k)/spl middot/p(n), for any elementary function f and any polynomial p, and under an assumption from parameterized complexity theory.