If, to the multiple choice knapsack problem, we add the constraint that each subset is of size " n " and remove the restriction on total weight, we get the "'assignment problem "', which is also the problem of finding a maximal "'bipartite matching " ':
32.
Then there exists a simple polynomial transformation of the class-teacher assignment problem with teacher availability constraints ( CTTA ) in school timetable construction to the PTCS problem : namely, map class instances to teacher instances, teacher instances to parent instances, time slots to time slots ( identity map ), and teacher availability to parent availability.
33.
If the numbers of agents and tasks are equal and the total cost of the assignment for all tasks is equal to the sum of the costs for each agent ( or the sum of the costs for each task, which is the same thing in this case ), then the problem is called the " linear assignment problem ".
