Improved Non-approximability Results for Vertex Cover with Density Constraints
COCOON '96 Proceedings of the Second Annual International Conference on Computing and Combinatorics
A 2-approximation NC algorithm for connected vertex cover and tree cover
Information Processing Letters
Approximating the dense set-cover problem
Journal of Computer and System Sciences
Approximating vertex cover on dense graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Parameterized Complexity of Vertex Cover Variants
Theory of Computing Systems
Facet defining inequalities among graph invariants: The system GraPHedron
Discrete Applied Mathematics
Enumerate and Expand: Improved Algorithms for Connected Vertex Cover and Tree Cover
Theory of Computing Systems
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 tight analysis of the maximal matching heuristic
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Improved approximation bounds for edge dominating set in dense graphs
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Approximating edge dominating set in dense graphs
Theoretical Computer Science
| Hi-index | 5.23 |
We consider the variant of the minimum vertex cover problem in which we require that the cover induces a connected subgraph. We give new approximation results for this problem in dense graphs, in which either the minimum or the average degree is linear. In particular, we prove tight parameterized upper bounds on the approximation returned by Savage's algorithm, and extend a vertex cover algorithm from Karpinski and Zelikovsky to the connected case. The new algorithm approximates the minimum connected vertex cover problem within a factor strictly less than 2 on all dense graphs. All these results are shown to be tight. Finally, we introduce the price of connectivity for the vertex cover problem, defined as the worst-case ratio between the sizes of a minimum connected vertex cover and a minimum vertex cover. We prove that the price of connectivity is bounded by 2/(1+@e) in graphs with average degree @en, and give a family of near-tight examples.