The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Easy problems for tree-decomposable graphs
Journal of Algorithms
Automata, Languages, and Machines
Automata, Languages, and Machines
The Complexity of First-Order and Monadic Second-Order Logic Revisited
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Improved Tree Decomposition Based Algorithms for Domination-like Problems
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Algorithm Design
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Enumerate and Expand: Improved Algorithms for Connected Vertex Cover and Tree Cover
Theory of Computing Systems
Fixed-parameter algorithms for the (k, r)-center in planar graphs and map graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Fast subexponential algorithm for non-local problems on graphs of bounded genus
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Known algorithms on graphs of bounded treewidth are probably optimal
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The Bidimensionality Theory and Its Algorithmic Applications 1
The Computer Journal
Catalan structures and dynamic programming in H-minor-free graphs
Journal of Computer and System Sciences
European Journal of Combinatorics
Model checking lower bounds for simple graphs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We introduce a variant of modal logic, named EXISTENTIAL COUNTING MODAL LOGIC (ECML), which captures a good number of problems known to be tractable in single exponential time when parameterized by treewidth. It appears that all these results can be subsumed by the theorem that model checking of ECML admits an algorithm with such complexity. We extend ECML by adding connectivity requirements and, using the Cut&Count technique introduced by Cygan et al. [4], prove that problems expressible in the extension are also tractable in single exponential time when parameterized by treewidth; however, using randomization. The need for navigational character of the introduced logic is informally justified by a negative result that two expository problems involving non-acyclic local conditions, Cl-VERTEX DELETION and GIRTH l VERTEX DELETION for l ≥ 5, do not admit such a robust algorithm unless Exponential Time Hypothesis fails.