k-NLC graphs and polynomial algorithms
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Edge dominating set and colorings on graphs with fixed clique-width
Discrete Applied Mathematics
Polynomial Time Recognition of Clique-Width \le \leq 3 Graphs (Extended Abstract)
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
The Tree-Width of Clique-Width Bounded Graphs Without Kn, n
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
How to Solve NP-hard Graph Problems on Clique-Width Bounded Graphs in Polynomial Time
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Algorithms for vertex-partitioning problems on graphs with fixed clique-width
Theoretical Computer Science
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Clique-width minimization is NP-hard
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Strong computational lower bounds via parameterized complexity
Journal of Computer and System Sciences
MSOL partitioning problems on graphs of bounded treewidth and clique-width
Theoretical Computer Science
On powers of graphs of bounded NLC-width (clique-width)
Discrete Applied Mathematics
Computing the Tutte Polynomial on Graphs of Bounded Clique-Width
SIAM Journal on Discrete Mathematics
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
On the Optimality of Planar and Geometric Approximation Schemes
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Finding Branch-Decompositions and Rank-Decompositions
SIAM Journal on Computing
Clique-width: on the price of generality
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Evaluations of Graph Polynomials
Graph-Theoretic Concepts in Computer Science
Planar Capacitated Dominating Set Is W[1]-Hard
Parameterized and Exact Computation
Computing graph polynomials on graphs of bounded clique-width
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
Width Parameters Beyond Tree-width and their Applications
The Computer Journal
On the complexity of some colorful problems parameterized by treewidth
Information and Computation
Maximal matching and path matching counting in polynomial time for graphs of bounded clique width
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Known algorithms on graphs of bounded treewidth are probably optimal
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The complexity of finding uniform sparsest cuts in various graph classes
Journal of Discrete Algorithms
Tight complexity bounds for FPT subgraph problems parameterized by clique-width
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Paths of bounded length and their cuts: Parameterized complexity and algorithms
Discrete Optimization
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
Lower bounds on the complexity of MSO1 model-checking
Journal of Computer and System Sciences
Digraph width measures in parameterized algorithmics
Discrete Applied Mathematics
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Many NP-hard problems can be solved efficiently when the input is restricted to graphs of bounded tree-width or clique-width. In particular, by the celebrated result of Courcelle, every decision problem expressible in monadic second order logic is fixed parameter tractable when parameterized by the tree-width of the input graph. On the other hand if we restrict ourselves to graphs of clique-width at most t, then there are many natural problems for which the running time of the best known algorithms is of the form nf(t), where n is the input length and f is some function. It was an open question whether natural problems like Graph Coloring, Max-Cut, Edge Dominating Set, and Hamiltonian Path are fixed parameter tractable when parameterized by the clique-width of the input graph. As a first step toward obtaining lower bounds for clique-width parameterizations, in [SODA 2009], we showed that unless FPT≠W[1], there is no algorithm with run time O(g(t) · nc), for some function g and a constant c not depending on t, for Graph Coloring, Edge Dominating Set and Hamiltonian Path. But the lower bounds obtained in [SODA 2009] are weak when compared to the upper bounds on the time complexity of the known algorithms for these problems when parameterized by the clique-width. In this paper, we obtain the asymptotically tight bounds for Max-Cut and Edge Dominating Set by showing that both problems • cannot be solved in time f(t)no(t), unless Exponential Time Hypothesis (ETH) collapses; and • can be solved in time nO(t), where f is an arbitrary function of t, on input of size n and clique-width at most t. We obtain our lower bounds by giving non-trivial structure-preserving "linear FPT reductions".