Enumerate and Expand: Improved Algorithms for Connected Vertex Cover and Tree Cover
Theory of Computing Systems
Computing the Tutte Polynomial in Vertex-Exponential Time
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Graph-Theoretic Concepts in Computer Science
Vertex and edge covers with clustering properties: Complexity and algorithms
Journal of Discrete Algorithms
Incompressibility through Colors and IDs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Almost 2-SAT is fixed-parameter tractable
Journal of Computer and System Sciences
Exact and approximate bandwidth
Theoretical Computer Science
Improved upper bounds for vertex cover
Theoretical Computer Science
Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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
Parameterized complexity of generalized vertex cover problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
On multiway cut parameterized above lower bounds
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Finding odd cycle transversals
Operations Research Letters
On Problems as Hard as CNF-SAT
CCC '12 Proceedings of the 2012 IEEE Conference on Computational Complexity (CCC)
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In the Connected Vertex Cover problem we are given an undirected graph G together with an integer k and we are to find a subset of vertices X of size at most k, such that X contains at least one end-point of each edge and such that X induces a connected subgraph. For this problem we present a deterministic algorithm running in O(2kpoly(n)) time and polynomial space, improving over the previous-best O(2.4882kpoly(n)) time deterministic algorithm and O(2kpoly(n)) time randomized algorithm. Furthermore, when usage of exponential space is allowed, we present an O(2kk(n+m)) time algorithm that solves a more general variant with real weights. Finally, we show that in O(2kpoly(n)) time and space one can count the number of connected vertex covers of size at most k, and this time upper bound can not be improved to O((2−ε)kpoly(n)) for any ε0 under the Strong Exponential Time Hypothesis, as shown by Cygan et al. [CCC'12].