The complexity of timetable construction problems

  • Tim B. Cooper
  • Jeffrey H. Kingston
Complexity Issues
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1153)


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.


timetable construction specification complexity 


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  1. [1]
    Tim B. Cooper and Jeffrey H. Kingston. The solution of real instances of the timetabling problem. The Computer Journal 36, 645–653 (1993).Google Scholar
  2. [2]
    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 Scholar
  3. [3]
    J. Csima. Investigations on a Time-Table Problem. Ph.D. thesis, School of Graduate Studies, University of Toronto, 1965.Google Scholar
  4. [4]
    S. Even, A. Itai, and A. Shamir. On the complexity of timetable and multicommodity flow problems. SIAM Journal on Computing 5, 691–703 (1976).Google Scholar
  5. [5]
    M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, 1979.Google Scholar
  6. [6]
    C.C. Gotlieb. The construction of class-teacher timetables. In Proc. IFIP Congress, pages 73–77, 1962.Google Scholar
  7. [7]
    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.Google Scholar
  8. [8]
    G. Schmidt and T. Ströhlein. Timetable construction — An annotated bibliography. The Computer Journal 23, 307–316 (1980).Google Scholar
  9. [9]
    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).Google Scholar
  10. [10]
    D. de Werra. Construction of school timetables by flow methods. INFOR — Canadian Journal of Operations Research and Information Processing 9, 12–22 (1971).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Tim B. Cooper
    • 1
  • Jeffrey H. Kingston
    • 1
  1. 1.Basser Department of Computer ScienceThe University of SydneyAustralia

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