We set the left part equal to the empty set so all the nodes are in the right part. And then we repeat the following operation: if exchanging the position of one node from one side to another side gives a better solution, that is the number of edges that go from one side to the other increases, then we switch the node. If we can exchange one node between V1 and V2 and this improve our solution, then we do this exchange. Otherwise, if there is not such node it means that we reach a local optimum.
It is a simple application of a local search technique, but even if simple it is possible to prove that this solution is 2-approximal solution. Basically, the idea is to prove that any local optimum is according to this scheme a 2-approximal solution.
