Define a bi$-$complete graph as a graph one whose vertex set can be partitioned into two disjoint subsets X and Y such that each of X and Y induces a complete graph.

Design an efficient brute force algorithm based on exhaustive search and that does not rely on depth first search or breadth first search to check whether a graph G$=($V$,$E$)$ is a bi$-$complete graph. You must ensure that the number of subsets the algorithm generates is minimized.

What is the big$-$Theta time cost of your algorithm? Explain your answer.