Approximating the tree and tour covers of a graph
Information Processing Letters
An improved fixed-parameter algorithm for vertex cover
Information Processing Letters
A general method to speed up fixed-parameter-tractable algorithms
Information Processing Letters
Faster exact algorithms for hard problems: a parameterized point of view
Discrete Mathematics
Vertex cover: further observations and further improvements
Journal of Algorithms
Introduction to Algorithms
Covering Problems with Hard Capacities
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Fast Fixed-Parameter Tractable Algorithms for Nontrivial Generalizations of Vertex Cover
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Approximation Algorithms for Partial Covering Problems
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Approximation Algorithms for Some Parameterized Counting Problems
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Computing small partial coverings
Information Processing Letters
On efficient fixed-parameter algorithms for weighted vertex cover
Journal of Algorithms
Solving large FPT problems on coarse-grained parallel machines
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
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Parameterized complexity: exponential speed-up for planar graph problems
Journal of Algorithms
Refined memorization for vertex cover
Information Processing Letters
Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
An improved approximation algorithm for vertex cover with hard capacities
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Upper bounds for vertex cover further improved
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Parameterized Complexity
Invitation to data reduction and problem kernelization
ACM SIGACT News
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Partial vs. Complete Domination: t-Dominating Set
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Faster Steiner Tree Computation in Polynomial-Space
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Improved Upper Bounds for Partial Vertex Cover
Graph-Theoretic Concepts in Computer Science
Vertex and edge covers with clustering properties: Complexity and algorithms
Journal of Discrete Algorithms
On problems without polynomial kernels
Journal of Computer and System Sciences
Journal of Discrete Algorithms
Complexity and approximation results for the connected vertex cover problem
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
A purely democratic characterization of W[1]
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Approximation of Partial Capacitated Vertex Cover
SIAM Journal on Discrete Mathematics
Enumerate and expand: improved algorithms for connected vertex cover and tree cover
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Triangles, 4-cycles and parameterized (in-)tractability
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Finding a minimum feedback vertex set in time O(1.7548n)
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Intuitive algorithms and t-vertex cover
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Deterministic parameterized connected vertex cover
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Linear problem kernels for NP-hard problems on planar graphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Efficient algorithms for the max k-vertex cover problem
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
Analytical models for risk-based intrusion response
Computer Networks: The International Journal of Computer and Telecommunications Networking
Parameterized complexity of 1-planarity
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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Important generalizations of the Vertex Cover problem (Connected Vertex Cover, Capacitated Vertex Cover, and Maximum Partial Vertex Cover) have been intensively studied in terms of approximability. However, their parameterized complexity has so far been completely open. We close this gap here by showing that, with the size of the desired vertex cover as parameter, Connected Vertex Cover and Capacitated Vertex Cover are both fixed-parameter tractable while Maximum Partial Vertex Cover is W[1]-hard. This answers two open questions from the literature. The results extend to several closely related problems. Interestingly, although the considered generalized Vertex Cover problems behave very similar in terms of constant-factor approximability, they display a wide range of different characteristics when investigating their parameterized complexities.