## Vertex Cover: Further Observations and Further Improvements (1999)

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Venue: | Journal of Algorithms |

Citations: | 150 - 14 self |

### BibTeX

@ARTICLE{Chen99vertexcover:,

author = {Jianer Chen and Iyad A. Kanj and Weijia Jia},

title = {Vertex Cover: Further Observations and Further Improvements},

journal = {Journal of Algorithms},

year = {1999},

volume = {41},

pages = {313--324}

}

### Years of Citing Articles

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### Abstract

Recently, there have been increasing interests and progresses in lowering the worst case time complexity for well-known NP-hard problems, in particular for the Vertex Cover problem. In this paper, new properties for the Vertex Cover problem are indicated and several simple and new techniques are introduced, which lead to an improved algorithm of time O(kn + 1:271 k k 2 ) for the problem. Our algorithm also induces improvement on previous algorithms for the Independent Set problem on graphs of small degree. 1 Introduction Many optimization problems from industrial applications are NP-hard. According to the NPcompleteness theory [10], these problems cannot be solved in polynomial time unless P = NP. However, this fact does not obviate the need for solving these problems for their practical importance. There has been a number of approaches to attacking the NP-hardness of optimization problems, including approximation algorithms, heuristic algorithms, and average time analysis. Recent...

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Citation Context ..., deciding if G has a vertex cover of k vertices), which is central in the study of fixed-parameter tractability theory [9] and has important applications in fields such as computational biochemistry =-=[15]. Buss d-=-eveloped the first fixed-parameter tractable algorithm of running time O�kn + 2 k k 2k+2 � for the problem (see [5]), which was later improved to O�kn + 2 k k 2 � by Downey and Fellows [10]. M... |

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