Years and Authors of Summarized Original Work
2001; Chen, Kanj, Jia
Problem Definition
The vertex cover problem is one of the six “basic” NP-complete problems according to Garey and Johnson [7]. Therefore, the problem cannot be solved in polynomial time unless \( { \mathrm{P}= } \) NP. However, the NP-completeness of the problem does not obviate the need for solving it because of its fundamental importance and wide applications.
One approach is to develop parameterized algorithms for the problem, with the computational complexity of the algorithms being measured in terms of both input size and a parameter value. This approach was initiated based on the observation that in many applications, the instances of the problem are associated with a small parameter. Therefore, by taking the advantages of the small parameters, one may be able to solve this NP-complete problem effectively and practically.
The problem is formally defined as follows. Let G be an (undirected) graph. A subset Cof...
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Abu-Khzam F, Collins R, Fellows M, Langston M, Suters W, Symons C (2004) Kernelization algorithms for the vertex cover problem: theory and experiments. In: Proceedings of the workshop on algorithm engineering and experiments (NLENEX), pp 62–69
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Chen, J. (2016). Vertex Cover Search Trees. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_462
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