Computational Complexity Issues in University Interview Timetabling

In the Department of Intelligence Science and Technology, Graduate School of Informatics, Kyoto University, there are approximately 20 professors, and 40 graduate course students in each year. In the final year of the course, every student submits a research thesis, and presents his/her work in twenty minutes to obtain a master degree. Presentation meeting is scheduled for two days, and in general, all professors attend the meeting and listen to all students’ presentation. For each student, three professors (usually from the same department) are assigned as a referee basically according to the presentation topic and professors’ research fields, and it is mandatory for referees to attend and evaluate the assigned students’ presentation. This presentation meeting used to be scheduled in one room, and there have been no serious problems. However, because of the increased number of graduate students, it became difficult to hold the meeting in two days this year, and we adopted a parallel session using two rooms. Then, there arises two major restrictions: (1) Two students evaluated by the same referee must be assigned to different timeslots. (2) Professors want to minimize the number of movements between rooms. Restriction (1) is a hard constraint, and the problem requires to decide if a feasible schedule exists. It is easy to see that this problem can be solved in polynomial time, and hence in this paper we focus on restriction (2), which is a soft constraint: We want to find a feasible schedule which minimizes the total number of movements of all professors. To understand the problem, consider the following small example: There are six students s1 through s6 and six professors p1 through p6. The assignment of professors to students is illustrated in Fig. 1: Student s1 is evaluated by two professors p1 and p2, and so on. One example of the schedule, say C1, is illustrated in Fig. 2. In C1, students s1 through s3, and students s4 through s6