Vertex Cover: Further Observations and Further Improvements

Recently, there have been increasing interests and progresses in lowering the worst case time complexity for well-known NP-hard problems, in particular for the VERTEX COVER problem. In this paper, new properties for the VERTEX COVER problem are indicated and several new techniques are introduced, which lead to a simpler and improved algorithm of time complexity O(kn + 1:271kk2) for the problem. Our algorithm also induces improvement on previous algorithms for the INDEPENDENT SET problem on graphs of small degree.

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