Six people, \(A\), \(B\), \(C\), \(D\), \(E\) and \(F\), are to be allocated to six tasks, 1, 2, 3, 4, 5 and 6. The following bipartite graph shows the tasks that each of the people is able to undertake.
\includegraphics{figure_1}
- Represent this information in an adjacency matrix. [2]
- Initially, \(B\) is assigned to task 5, \(D\) to task 2, \(E\) to task 4 and \(F\) to task 3.
Demonstrate, by using an algorithm from this initial matching, how each person can be allocated to a task. [5]