Keywords and Synonyms
Vertex cover preprocessing; Vertex cover data reduction
Problem Definition
Let G be an undirected graph. A subset C of vertices in G is a vertex cover for G if every edge in G has at least one end in C. The (parametrized) vertex cover problem is for each given instance (G, k), where G is a graph and \( { k \geq 0 } \) is an integer (the parameter), to determine whether the graph G has a vertex cover of at most k vertices.
The vertex cover problem is one of the six “basic” NP-complete problems according to Garey and Johnson [4]. Therefore, the problem cannot be solved in polynomial time unless 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 was initiated based on the observation that in many applications, the parameter kis small. Therefore, by taking the advantages of this fact, one may be able to solve this NP-complete problem...
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Abu-Khzam, F., Collins, R., Fellows, M., Langston, M., Suters, W., Symons, C.: Kernelization algorithms for the vertex cover problem: theory and experiments. In: Proc. Workshop on Algorithm Engineering and Experiments (ALENEX) pp. 62–69 (2004)
Bar-Yehuda, R., Even, S.: A local-ratio theorem for approximating the weighted vertex cover problem. Ann. Discret. Math. 25, 27–45 (1985)
Chen, J., Kanj, I.A., Jia, W.: Vertex cover: further observations and further improvements. J. Algorithm 41, 280–301 (2001)
Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco (1979)
Nemhauser, G.L., Trotter, L.E.: Vertex packing: structural properties and algorithms. Math. Program. 8, 232–248 (1975)
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© 2008 Springer-Verlag
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Chen, J. (2008). Vertex Cover Kernelization. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_460
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DOI: https://doi.org/10.1007/978-0-387-30162-4_460
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-30770-1
Online ISBN: 978-0-387-30162-4
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