Abstract
We present a simple LP-free (i.e., not requiring linear programming) approximation algorithm for the minimum weight vertex cover problem. Our new approximation algorithm does not need to solve a linear programming problem, nor such a formulation is needed to establish its approximation bound. The algorithm takes linear time with respect to the number of nodes and edges in the graph, and generates solutions that are within twice the weight of a minimum weight vertex cover. Both the algorithm and its proof of correctness are elegant and simple.
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