Cal Poly RSS

It has often been said that the problem of creating timetables for scheduling university courses is hard, even as hard as solving an NP-Complete problem. There are many papers in the literature that make this assertion but rarely are precise problem definitions provided and no papers were found which offered proofs that the university course scheduling problem being discussed is NP-Complete.This thesis defines a scheduling problem that has realistic constraints. It schedules professors to sections of courses they are willing to teach at times when they are available without overloading them. Both decision and optimization versions are precisely defined. An algorithm is then provided which solves the optimization problem in polynomial time. From this it is concluded that the decision problem is unlikely to be NP-Complete because indeed it is in P. A second more complex timetable design problem, that additionally seeks to assign appropriate rooms in which the professors can teach the courses, is then introduced. Here too both decision and optimization versions are defined. The second major contribution of this thesis is to prove that this decision problem is NP-Complete and hence the corresponding optimization problem is NP-Hard.

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