Many problems that arise in operations research and related fields are combinatorial in nature: problems where we seek the optimum from a very large but finite number of solutions. Sometimes such problems can be solved quickly and efficiently, but often the best solution procedures available are slow and tedious. It therefore becomes important to assess how well a proposed procedure will perform.
The theory of computational complexity addresses this issue. Complexity theory is a comparatively young field, with seminal papers dating from 1971–1972 ([1], [5]). Today, it is a wide field encompassing many subfields. For a formal treatment, see [6]. As we shall see, the theory partitions all realistic problems into two groups: the ‘easy’ and the ‘hard’ to solve, depending on how complex (hence how fast or slow) the computational procedure for that problem is. The theory defines still other classes, but all but the most artificial mathematical constructs fall into these two. Each of them...
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Cook, S.A.: ‘The complexity of theorem proving procedures’, Proc. 3rd Annual ACM Symposium on Theory of Computing, ACM, 1971, pp. 151–158.
Garey, M.R., and Johnson, D.S.: Computers and intractability, Freeman, 1979.
Hardy, G.H., and Wright, E.M.: An introduction to the theory of numbers, Clarendon Press, 1979.
Hopcroft, J.E., and Ullman, J.D.: Introduction to automata theory, languages, and computation, Addison-Wesley, 1979.
Karp, R.M.: ‘Reducibility among combinatorial problems’, in R.E. Miller and J.W. Thatcher (eds.): Complexity of Computer Computations, Plenum, 1972, pp. 85–103.
Papadimitriou, C.H.: Computational complexity, Addison-Wesley, 1994.
Pinedo, M.: Scheduling: Theory, algorithms and systems, Prentice-Hall, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Kluwer Academic Publishers
About this entry
Cite this entry
Emmons, H., Rai, S. (2001). Computational Complexity Theory . In: Floudas, C.A., Pardalos, P.M. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/0-306-48332-7_67
Download citation
DOI: https://doi.org/10.1007/0-306-48332-7_67
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-6932-5
Online ISBN: 978-0-306-48332-5
eBook Packages: Springer Book Archive