Improved Upper Bounds for Partial Vertex Cover

The Partial Vertex Cover problem is to decide whether a graph contains at most k nodes covering at least t edges. We present deterministic and randomized algorithms with run times of O *(1.396 t ) and O *(1.2993 t ), respectively. For graphs of maximum degree three, we show how to solve this problem in O *(1.26 t ) steps. Finally, we give an O *(3 t ) algorithm for Exact Partial Vertex Cover , which asks for at most k nodes covering exactly t edges.

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