TY - JOUR

T1 - An extension of the Nemhauser-Trotter theorem to generalized vertex coverwith applications

AU - Bar-Yehuda, Reuven

AU - Hermelin, Danny

AU - Rawitz, Dror

PY - 2010

Y1 - 2010

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 polynomial-time approximation scheme (PTAS) for planar graphs, a (2 - lglg n/2lg 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 polynomial-time approximation scheme (PTAS) for planar graphs, a (2 - lglg n/2lg n)-approximation algorithm for general graphs, and a 2k kernel for the parameterized Generalized Vertex Cover problem.

KW - Approximation algorithms

KW - Generalized vertex cover

KW - Local ratio technique

KW - Nemhauser-trotter theorem

UR - http://www.scopus.com/inward/record.url?scp=77952538417&partnerID=8YFLogxK

U2 - 10.1137/090773313

DO - 10.1137/090773313

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AN - SCOPUS:77952538417

SN - 0895-4801

VL - 24

SP - 287

EP - 300

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 1

ER -