Polynomial reduction of time-space scheduling to time scheduling

Authors:
J. Studenovský
Affiliations:
Institute of Informatics, P.J. Šafárik University, Jesenná 5, 04154 Košice, Slovakia
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

We study the University Course Timetabling Problem (UCTP). In particular we deal with the following question: is it possible to decompose UCTP into two problems, namely, (i) a time scheduling, and (ii) a space scheduling. We have arguments that it is not possible. Therefore we study UCTP with the assumption that each room belongs to exactly one type of room. A type of room is a set of rooms, which have similar properties. We prove that in this case UCTP is polynomially reducible to time scheduling. Hence we solve UCTP with the following method: at first we solve time scheduling and subsequently we solve space scheduling with a polynomial O(n^3) algorithm. In this way we obtain a radical (exponential) speed-up of algorithms for UCTP. The method was applied at P.J. Safarik University.