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

Reuven Bar-Yehuda; Danny Hermelin; Dror Rawitz

doi:10.1007/978-3-642-12450-1_2

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

Reuven Bar-Yehuda, Danny Hermelin, Dror Rawitz

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

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
Title of host publication	Approximation and Online Algorithms - 7th International Workshop, WAOA 2009, Revised Papers
Pages	13-24
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-12450-1_2
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

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5893 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	7th Workshop on Approximation and Online Algorithms, WAOA 2009
Country/Territory	Denmark
City	Copenhagen
Period	10/09/09 → 11/09/09

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

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

Cite this

Bar-Yehuda, R., Hermelin, D., & Rawitz, D. (2009). Extension of the nemhauser and trotter theorem to generalized vertex cover with applications. In Approximation and Online Algorithms - 7th International Workshop, WAOA 2009, Revised Papers (pp. 13-24). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5893 LNCS). https://doi.org/10.1007/978-3-642-12450-1_2

Bar-Yehuda, Reuven ; Hermelin, Danny ; Rawitz, Dror. / Extension of the nemhauser and trotter theorem to generalized vertex cover with applications. Approximation and Online Algorithms - 7th International Workshop, WAOA 2009, Revised Papers. 2009. pp. 13-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Extension of the nemhauser and trotter theorem to generalized vertex cover with applications",

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.",

author = "Reuven Bar-Yehuda and Danny Hermelin and Dror Rawitz",

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Bar-Yehuda, R, Hermelin, D & Rawitz, D 2009, Extension of the nemhauser and trotter theorem to generalized vertex cover with applications. in Approximation and Online Algorithms - 7th International Workshop, WAOA 2009, Revised Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5893 LNCS, pp. 13-24, 7th Workshop on Approximation and Online Algorithms, WAOA 2009, Copenhagen, Denmark, 10/09/09. https://doi.org/10.1007/978-3-642-12450-1_2

Extension of the nemhauser and trotter theorem to generalized vertex cover with applications. / Bar-Yehuda, Reuven; Hermelin, Danny; Rawitz, Dror.
Approximation and Online Algorithms - 7th International Workshop, WAOA 2009, Revised Papers. 2009. p. 13-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5893 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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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.

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Bar-Yehuda R, Hermelin D, Rawitz D. Extension of the nemhauser and trotter theorem to generalized vertex cover with applications. In Approximation and Online Algorithms - 7th International Workshop, WAOA 2009, Revised Papers. 2009. p. 13-24. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-12450-1_2

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

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