Optimal = {g, h}

Approximate = {a, g, d, h}

The size of the approximate vertex cover is never more than twice the size of the optimal vertex cover.

**Theorem 37.1**

Approx-Vertex-Cover has a ratio bound of 2.

**Proof:**

The approximate solution C is a vertex cover.

Let A be the set of edges chosen by the algorithm. Since each such edge's endpoints were not in C at the time, C = 2A. An optimal cover must have at least A vertices, C*A. Thus C* 1/2C and 2 = p.