Abstract
This paper shows that timetable construction is NP-complete in a number of quite different ways that arise in practice, and discusses the prospects of overcoming these problems. A formal specification of the problem based on TTL, a timetable specification language, is given.
Specificially, we show that NP-completeness arises whenever students have a wide subject choice, or meetings vary in duration, or simple conditions are imposed on the choice of times for meetings, such as requirements for double times or an even spread through the week. In realistic cases, the assignment of meetings to just one teacher (after their times are fixed) is NP-complete. And although suitable times can be assigned to all the meetings involving one student group simultaneously, the corresponding problem for two student groups is NP-complete.
Keywords
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Tim B. Cooper and Jeffrey H. Kingston. The solution of real instances of the timetabling problem. The Computer Journal 36, 645–653 (1993).
Tim B. Cooper and Jeffrey H. Kingston. A program for constructing high school timetables. In First International Conference on the Practice and Theory of Automated Timetabling. Napier University, Edinburgh, UK, 1995. Also ftp://ftp.cs.su.oz.au/pub/tr/TR95_496.ps.Z.
J. Csima. Investigations on a Time-Table Problem. Ph.D. thesis, School of Graduate Studies, University of Toronto, 1965.
S. Even, A. Itai, and A. Shamir. On the complexity of timetable and multicommodity flow problems. SIAM Journal on Computing 5, 691–703 (1976).
M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, 1979.
C.C. Gotlieb. The construction of class-teacher timetables. In Proc. IFIP Congress, pages 73–77, 1962.
R. M. Karp. Reducibility among combinatorial problems. In R. E. Miller and J. W. Thatcher (eds.), Complexity of Computer Computations, pages 85–103. Plenum Press, New York, 1972.
G. Schmidt and T. Ströhlein. Timetable construction — An annotated bibliography. The Computer Journal 23, 307–316 (1980).
D. J. A. Welsh and M. B. Powell. An upper bound for the chromatic number of a graph and its application to timetabling problems. The Computer Journal 10, 85–86 (1967).
D. de Werra. Construction of school timetables by flow methods. INFOR — Canadian Journal of Operations Research and Information Processing 9, 12–22 (1971).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cooper, T.B., Kingston, J.H. (1996). The complexity of timetable construction problems. In: Burke, E., Ross, P. (eds) Practice and Theory of Automated Timetabling. PATAT 1995. Lecture Notes in Computer Science, vol 1153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61794-9_66
Download citation
DOI: https://doi.org/10.1007/3-540-61794-9_66
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61794-5
Online ISBN: 978-3-540-70682-3
eBook Packages: Springer Book Archive