## Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 13-24 |

Number of pages | 12 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

DOIs | |

State | Published - 1 Dec 2009 |

Externally published | Yes |

Event | 7th Workshop on Approximation and Online Algorithms, WAOA 2009 - Copenhagen, Denmark Duration: 10 Sep 2009 → 11 Sep 2009 |