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.
|Number of pages||12|
|Journal||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|State||Published - 1 Dec 2009|
|Event||7th Workshop on Approximation and Online Algorithms, WAOA 2009 - Copenhagen, Denmark|
Duration: 10 Sep 2009 → 11 Sep 2009