Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Algorithms for facility location problems with outliers
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Vertex cover: further observations and further improvements
Journal of Algorithms
The importance of being biased
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP
Journal of the ACM (JACM)
On the Equivalence between the Primal-Dual Schema and the Local Ratio Technique
SIAM Journal on Discrete Mathematics
The minimum generalized vertex cover problem
ACM Transactions on Algorithms (TALG)
A unified approach to approximating partial covering problems
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
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The Nemhauser-Trotter theorem provides an algorithm which is frequently used as a subroutine in approximation algorithms for the classical Vertex Cover problem. In this paper we present an extension of this theorem so it fits a more general variant of Vertex Cover, namely, the Generalized Vertex Cover problem, where edges are allowed not to be covered at a certain predetermined penalty. We show that many applications of the original Nemhauser-Trotter theorem can be applied using our extension to Generalized Vertex Cover. These applications include a $(2-2/d)$-approximation algorithm for graphs of bounded degree $d$, a polynomial-time approximation scheme (PTAS) for planar graphs, a $(2-\lg\lg n/2\lg n)$-approximation algorithm for general graphs, and a $2k$ kernel for the parameterized Generalized Vertex Cover problem.