Consider the following problem:
Input: a complete bipartite graph $G$ with its edges colored either white or black, a number $k$.
Output: a subset of vertices $W$ of size $k$ which maximizes the following:
number of black edges with both endpoints in $W$ + number of white edges with at most one endpoint in $W$
What is the complexity of this problem? Is there a polynomial time algorithm (exact or approximate) for the problem? Could this problem be reduced to any classic Thoeretical CS problem, like the Max-Cut?