# Algorithmic Meta Theorems for Sparse Graph Classes

@inproceedings{Grohe2014AlgorithmicMT, title={Algorithmic Meta Theorems for Sparse Graph Classes}, author={Martin Grohe}, booktitle={CSR}, year={2014} }

Algorithmic meta theorems give efficient algorithms for classes of algorithmic problems, instead of just individual problems. They unify families of algorithmic results obtained by similar techniques and thus exhibit the core of these techniques. The classes of problems are typically defined in terms of logic and structural graph theory. A well-known example of an algorithmic meta theorem is Courcelle’s Theorem, stating that all properties of graphs of bounded tree width that are definable in…

## 5 Citations

### Deciding first-order properties of nowhere dense graphs

- Mathematics, Computer ScienceSTOC
- 2014

It is shown that deciding properties of graphs definable in first-order logic is fixed-parameter tractable on nowhere dense graph classes, and a "rank-preserving" version of Gaifman's locality theorem is proved.

### On the Width of Regular Classes of Finite Structures

- Mathematics, Computer ScienceCADE
- 2019

It is shown that the problem of counting satisfying assignments for a first-order logic formula in a structure of constant width is fixed parameter tractable when parameterized by the width parameter and can be solved in quadratic time with respect to the length of the input representation of the structure.

### The parameterized space complexity of model-checking bounded variable first-order logic

- Computer ScienceLog. Methods Comput. Sci.
- 2019

The parameterized model-checking problem for a class of first-order sentences (queries) asks to decide whether a given sentence from the class holds true in a given relational structure (database) and is studied under the assumption that Savitch's Theorem is optimal.

### Symbolic Solutions for Symbolic Constraint Satisfaction Problems

- Computer Science, MathematicsKR
- 2020

The main result states that given an ordered decision diagram D of length k and width w specifying a CSP instance, one can determine in time f(w,w′) · k whether there is an ODD of width at most w′ encoding a solution for this instance.

### Deciding First-Order Properties of Nowhere Dense Graphs

- Mathematics, Computer ScienceJ. ACM
- 2017

The proofs are based on a new game-theoretic characterization of nowhere dense graphs that allows for a recursive version of locality-based algorithms on these classes and prove a “rank-preserving” version of Gaifman’s locality theorem.

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