A polynomial time 3 2 -approximation algorithm for the vertex cover problem on a class of graphs

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We develop a polynomial time 3/2-approximation algorithm to solve the vertex cover problem on a class of graphs satisfying a property called ``active edge hypothesis''. The algorithm also guarantees an optimal solution on specially structured graphs. Further, we give an extended algorithm which guarantees a vertex cover S₁ on an arbitrary graph such that |S₁|≤ 3/2 |S*|+ξ where S* is an optimal vertex cover and ξ is an error bound identified by the algorithm. We obtained ξ= 0 for all the test problems we have considered which include specially constructed instances that were expected to be hard. So far we could not construct a graph that gives ξ= 0.