Vertex Cover Kernelization
 Jianer Chen
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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” NPcomplete problems according to Garey and Johnson [4]. Therefore, the problem cannot be solved in polynomial time unless P \( { = } \) NP. However, the NPcompleteness 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 k is small. Therefo ...
 AbuKhzam, 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)
 BarYehuda, R., Even, S. (1985) A localratio theorem for approximating the weighted vertex cover problem. Ann. Discret. Math. 25: pp. 2745
 Chen, J., Kanj, I.A., Jia, W. (2001) Vertex cover: further observations and further improvements. J. Algorithm 41: pp. 280301 CrossRef
 Garey, M., Johnson, D. (1979) Computers and Intractability: A Guide to the Theory of NPcompleteness. Freeman, San Francisco
 Nemhauser, G.L., Trotter, L.E. (1975) Vertex packing: structural properties and algorithms. Math. Program. 8: pp. 232248 CrossRef
 Title
 Vertex Cover Kernelization
 Reference Work Title
 Encyclopedia of Algorithms
 Pages
 pp 199
 Copyright
 2008
 DOI
 10.1007/9780387301624_460
 Print ISBN
 9780387307701
 Online ISBN
 9780387301624
 Publisher
 Springer US
 Copyright Holder
 SpringerVerlag
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 Editors
 Editor Affiliations

 1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University
 Authors

 Jianer Chen ^{(1)}
 Author Affiliations

 1. Department of Computer Science, Texas A&M University, College Station, TX, USA
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