Abstract
The problem instance of Vertex Cover consists of an undirected graph G = (V, E) and a positive integer k, the question is whether there exists a subset C ⊂-V of vertices such that each edge in E has at least one of its endpoints in C with |C|≤ k. We improve two recent worst case upper bounds for Vertex Cover. First, Balasubramanian et al. showed that Vertex Cover can be solved in time O(kn + 1.32472k k 2), where n is the number of vertices in G. Afterwards, Downey et al. improved this to O(kn + 1.31951k k 2). Bringing the exponential base significantly below 1.3, we present the new upper bound O(kn + 1.29175k k 2).
Supported by a Feodor Lynen fellowship of the Alexander von Humboldt-Stiftung, Bonn, and the Center for Discrete Mathematics, Theoretical Computer Science and Applications (DIMATIA), Prague, Czech Republic.
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Niedermeier, R., Rossmanith, P. (1999). Upper Bounds for Vertex Cover Further Improved. In: Meinel, C., Tison, S. (eds) STACS 99. STACS 1999. Lecture Notes in Computer Science, vol 1563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49116-3_53
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DOI: https://doi.org/10.1007/3-540-49116-3_53
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