The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Spanning trees with many leaves
SIAM Journal on Discrete Mathematics
Easy problems for tree-decomposable graphs
Journal of Algorithms
Deciding first-order properties of locally tree-decomposable structures
Journal of the ACM (JACM)
Approximation Schemes for First-Order Definable Optimisation Problems
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Clique-width: on the price of generality
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Graph Layout Problems Parameterized by Vertex Cover
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number
Theory of Computing Systems - Special Issue: Computation and Logic in the Real World; Guest Editors: S. Barry Cooper, Elvira Mayordomo and Andrea Sorbi
On brambles, grid-like minors, and parameterized intractability of monadic second-order logic
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Improved parameterized upper bounds for vertex cover
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Width Parameters Beyond Tree-width and their Applications
The Computer Journal
Hitting and harvesting pumpkins
ESA'11 Proceedings of the 19th European conference on Algorithms
Twin-Cover: beyond vertex cover in parameterized algorithmics
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
When trees grow low: shrubs and fast MSO1
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Preprocessing subgraph and minor problems: when does a small vertex cover help?
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Parameterized maximum path coloring
Theoretical Computer Science
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Possibly the most famous algorithmic meta-theorem is Courcelle's theorem, which states that all MSO-expressible graph properties are decidable in linear time for graphs of bounded treewidth. Unfortunately, the running time's dependence on the formula describing the problem is in general a tower of exponentials of unbounded height, and there exist lower bounds proving that this cannot be improved even if we restrict ourselves to deciding FO logic on trees. We investigate whether this parameter dependence can be improved by focusing on two proper subclasses of the class of bounded treewidth graphs: graphs of bounded vertex cover and graphs of bounded max-leaf number. We prove stronger algorithmic meta-theorems for these more restricted classes of graphs. More specifically, we show it is possible to decide any FO property in both of these classes with a singly exponential parameter dependence and that it is possible to decide MSO logic on graphs of bounded vertex cover with a doubly exponential parameter dependence. We also prove lower bound results which show that our upper bounds cannot be improved significantly, under widely believed complexity assumptions. Our work addresses an open problem posed by Michael Fellows.