Upper bounds for vertex cover further improved

Authors:
Rolf Niedermeier;Peter Rossmanith
Affiliations:
Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Tübingen, Fed. Rep. of Germany;Institut für Informatik, Technische Universität München, München, Fed. Rep. of Germany
Venue:
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Year:
1999

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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+1:32472kk2), where n is the number of vertices in G. Afterwards, Downey et al. improved this to O(kn+1:31951kk2). Bringing the exponential base significantly below 1:3, we present the new upper bound O(kn+1:29175kk2).