SIAM Journal on Computing
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Fixed Parameter Algorithms for PLANAR DOMINATING SET and Related Problems
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
On the existence of subexponential parameterized algorithms
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Tight lower bounds for certain parameterized NP-hard problems
Information and Computation
An O(2O(k)n3) FPT algorithm for the undirected feedback vertex set problem*
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Parameterized Complexity
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A (k,r)-tuple is a word of length r on an alphabet of size k. A graph is (k,r)-representable if we can assign a (k,r)-tuple to each vertex such that two vertices are connected iff the associated tuples agree on some component. We study the complexity of several graph problems on (k,r)-representable graphs, as a function of the parameters k,r; the problems under study are Maximum Independent Set, Minimum Dominating Set and Maximum Clique. In this framework, there are two classes of interest: the graphs representable with tuples of logarithmic length (i.e. graphs (k,r)-representable with r = O(k logn)), and the graphs representable with tuples of polynomial length (i.e. graphs (k,r)-representable with r = poly(n)). In both cases, we show that the problems are computationally hard, though we obtain stronger hardness results in the second case. Our hardness results also allow us to derive optimality results for Multidimensional Matching and Disjoint r-Subsets.