TY - GEN

T1 - Extension of the nemhauser and trotter theorem to generalized vertex cover with applications

AU - Bar-Yehuda, Reuven

AU - Hermelin, Danny

AU - Rawitz, Dror

PY - 2009

Y1 - 2009

N2 - 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 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.

AB - 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 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.

UR - http://www.scopus.com/inward/record.url?scp=78651234596&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-12450-1_2

DO - 10.1007/978-3-642-12450-1_2

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AN - SCOPUS:78651234596

SN - 3642124496

SN - 9783642124495

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 13

EP - 24

BT - Approximation and Online Algorithms - 7th International Workshop, WAOA 2009, Revised Papers

T2 - 7th Workshop on Approximation and Online Algorithms, WAOA 2009

Y2 - 10 September 2009 through 11 September 2009

ER -