Use three methods to find the vertex cover of the graph.

Reduce vertex_cover problem to SAT problem. Then use minisat to find the satisfied assignment. This method find the minimum vertex_cover.

Find the vertex with biggest degree, remove edges related to it and add this vertex to vertex_cover set. Keep doning this until all the edges are removed.

Randomly pick a edge<u,v>. Remove edges related to u and v and add u, v to vertex_cover set. Keep doing this until all the edges are removed.