Upper Bounds for Vertex Cover Further Improved

Niedermeier, Rolf; Rossmanith, Peter

doi:10.1007/3-540-49116-3_53

Cited by 85 publications

(75 citation statements)

References 7 publications

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“…In addition, the problem has been a central problem in the study of parameterized algorithms [11], and has applications in areas such as computational biochemistry and biology [6]. Since the development of the first parameterized algorithm for the problem by Sam Buss which runs in O(kn + 2 k k 2k+2 ) time [3], there has been an impressive list of improved algorithms for the problem [1,7,8,10,17,18,20]. The most recent algorithm for the problem running in polynomial space was presented in 1999 and gives the currently best time upper bound of O(kn + 1.286 k ) [7].…”

Section: Introductionmentioning

confidence: 99%

Improved Parameterized Upper Bounds for Vertex Cover

Chen

Kanj

Xia

2006

Lecture Notes in Computer Science

106

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Section: Introductionmentioning

confidence: 99%

Improved Parameterized Upper Bounds for Vertex Cover

Chen

Kanj

Xia

2006

Lecture Notes in Computer Science

106

View full text Add to dashboard Cite

“…This is also due to its applications in fields like computational biochemistry [16]. Since the development of the first parameterized algorithm by Sam Buss, which has running time O(kn + 2 k k 2k+2 ) and was decribed in [4], there has been an impressive list of improved algorithms for the problem [2,6,7,9,18,21]. Currently, the best parameterized algorithm for Vertex Cover has running time O(kn + 1.285 k ) for general graphs [6], and the best parameterized algorithm for Vertex Cover on degree-3 graphs has running time O(kn + 1.237 k ) [7].…”

Section: Introductionmentioning

confidence: 99%

“…As we mentioned before, Vertex Cover and Maximum Independent Set are among the most extensively studied NP-hard problems with many proposed algorithms [2,4,6,9,13,18,19,20,21,23]. In particular, Vertex Cover and Maximum Independent Set on graphs of degrees 3 and 4 have received a lot of attention recently [3,6,7].…”

Section: Introductionmentioning

confidence: 99%

“…In spite of the restriction imposed on graph degrees (being bounded by 3 or 4), improvements on the previous upper bounds for these problems can be challenging and meticulous. Moreover, most of the algorithms for Vertex Cover and Maximum Independent Set on general graphs end up reducing the problem to that on low-degree graphs [6,18,19]. Thus, a simple and uniform algorithm that induces significant improvements on the existing bounds for these problems is of high interest, and shows the power and effectiveness of the new analysis and algorithmic methods.…”

Section: Introductionmentioning

confidence: 99%

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Labeled Search Trees and Amortized Analysis: Improved Upper Bounds for NP-Hard Problems

2005

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A sequence of exact algorithms to solve the Vertex Cover and Maximum Independent Set problems have been proposed in the literature. All these algorithms appeal to a very conservative analysis that considers the size of the search tree, under a worst-case scenario, to derive an upper bound on the running time of the algorithm. In this paper we propose a different approach to analyze the size of the search tree. We use amortized analysis to show how simple algorithms, if analyzed properly, may perform much better than the upper bounds on their running time derived by considering only a worst-case scenario. This approach allows us to present a simple algorithm of running time O(1.194 k k 2 + n) for the parameterized Vertex Cover problem on degree-3 graphs, and a simple algorithm of running time O(1.1255 n ) for the Maximum Independent Set problem on degree-3 graphs. Both algorithms improve the previous best algorithms for the problems.

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“…Furthermore, the minimum vertex cover problem remains NPcomplete even for certain restricted graphs, for example, the bounded degree graphs (3) . Because the minimum vertex cover problem has many important practical applications, especially in multiple sequence alignments for computational biochemistry (4) (5) , the problem has been widely studied by many researchers. Garey and Johnson (6) presented a simple approximation algorithm based on maximal matching for the general graphs.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Algorithm for Minimum Vertex Cover Problem

Wang

Tang

2004

IEEJ Trans.EIS

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An efficient parallel algorithm for solving the minimum vertex cover problem using binary neural network is presented. The proposed algorithm which is designed to find the smallest vertex cover of a graph, uses the binary neural network to get a near-smallest vertex cover of the graph, and adjusts the balance between the constraint term and the cost term of the energy function to help the network escape from the state of the near-smallest vertex cover to the state of the smallest vertex cover or better one. The proposed algorithm is tested on a large number of random graphs and benchmark graphs. The simulation results show that the proposed algorithm is very satisfactory and better than previous works for solving the minimum vertex cover problem.

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Upper Bounds for Vertex Cover Further Improved

Cited by 85 publications

References 7 publications

Improved Parameterized Upper Bounds for Vertex Cover

Improved Parameterized Upper Bounds for Vertex Cover

Labeled Search Trees and Amortized Analysis: Improved Upper Bounds for NP-Hard Problems

An Efficient Algorithm for Minimum Vertex Cover Problem

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