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

Reuven Bar-Yehuda, Danny Hermelin, Dror Rawitz

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish
Pages (from-to)287-300
Number of pages14
JournalSIAM Journal on Discrete Mathematics
Issue number1
StatePublished - 2010
Externally publishedYes


  • Approximation algorithms
  • Generalized vertex cover
  • Local ratio technique
  • Nemhauser-trotter theorem


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