Peer grading.
For the final exam at the Arbutus Culinary Masters Institute (ACMI),
each student must prepare a meal of k dishes. Since the
instructor cannot taste the work of all the students, the dishes are
actually evaluated by other students. As always there are complications:
- A student must not evaluate his/her own work.
- Each of the k dishes must be evaluated by 3 different
people.
- No one should be asked to evaluate more than d dishes.
- A student can only evaluate the work of another student
who has similar grades. (This is the "peer" part of peer grading.)
Here two students have similar grades if their GPAs are
within 0.500.
The peer grading problem is to assign to each student a list
of dishes to evaluate so that all of the requirements and constraints
described above are satisfied.
Given a list of n students and their GPAs
g_{1},
g_{2},
g_{3},
...
g_{n},
describe how you can construct a flow network
G = ( V, E ) with a capacity
function c such that the maximum flow in the flow network
helps solve the peer grading problem at ACMI. Describe what the vertices,
edges and capacities represent. Explain how the maximum flow in G
corresponds to a solution to the peer grading problem.