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

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| ≤ 32 |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 6= 0.