Connected Vertex Covers in Dense Graphs
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Parameterized Complexity for Domination Problems on Degenerate Graphs
Graph-Theoretic Concepts in Computer Science
Incompressibility through Colors and IDs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Connected vertex covers in dense graphs
Theoretical Computer Science
Capacitated domination and covering: a parameterized perspective
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Parameterized algorithm for eternal vertex cover
Information Processing Letters
The curse of connectivity: t-total vertex (edge) cover
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Subexponential algorithms for partial cover problems
Information Processing Letters
Improved approximations for hard optimization problems via problem instance classification
Rainbow of computer science
Implicit branching and parameterized partial cover problems
Journal of Computer and System Sciences
Parameterized reductions and algorithms for another vertex cover generalization
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Efficient algorithms for network localization using cores of underlying graphs
ALGOSENSORS'11 Proceedings of the 7th international conference on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities
Fixed-parameter tractability for the subset feedback set problem and the S-cycle packing problem
Journal of Combinatorial Theory Series B
Parameterized reductions and algorithms for a graph editing problem that generalizes vertex cover
Theoretical Computer Science
On the k-edge-incident subgraph problem and its variants
Discrete Applied Mathematics
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Important variants of theVERTEX COVER problem (among others, CONNECTED VERTEX COVER, CAPACITATED VERTEX COVER, and MAXIMUM PARTIAL VERTEX COVER) have been intensively studied in terms of polynomial-time approximability. By way of contrast, their parameterized complexity has so far beencompletely open. We close this gap here by showing that, with the size of the desired vertex cover as the parameter, CONNECTED VERTEX COVER and CAPACITATED VERTEX COVER are both fixed-parameter tractable while MAXIMUM PARTIAL VERTEX COVER is W[1]-complete. This answers two open questions from the literature. The results extend to several closely related problems. Interestingly, although the considered variants of VERTEX COVER behave very similar in terms of constant factor approximability, they display a wide range of different characteristics when investigating their parameterized complexities.