The term “ computational complexity” has two usages which must be distinguished. On the one hand, it refers to an algorithm for solving instances of a problem: broadly stated, the computational complexity of an algorithm is a measure of how many steps the algorithm will require in the worst case for an instance or input of a given size. The number of steps is measured as a function of that size.
The term's second, more important use is in reference to a problem itself. The theory of computational complexity involves classifying problems according to their inherent tractability or intractability — that is, whether they are “easy” or “hard” to solve. This classification scheme includes the well-known classes P and NP; the terms “NP-complete” and “NP-hard” are related to the class NP.
ALGORITHMS AND COMPLEXITY
To understand what is meant by the complexity of an algorithm, we must define algorithms, problems, and problem instances. Moreover, we must understand how one measures the size of...
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
Bovet, D. P. and Crescenzi, P. (1994). Introduction to the Theory of Complexity. Prentice-Hall, Englewood Cliffs, New Jersey.
Cook, S. A. (1971). “The complexity of theorem-proving procedures,” Proc. 3rd Annual ACM Symp. Theory of Computing, 151–158.
Garey, M. R. and Johnson, D. S. (1979). Computers and Intractability: a Guide to the Theory of NP-Completeness. W.H. Freeman, New York.
Karp, R. M. (1975). “On the computational complexity of combinatorial problems,” Networks 5, 45–68.
Lewis, H. R. and Papadimitriou, C. H. (1997). Elements of the Theory of Computation, 2nd ed. Prentice-Hall, Englewood Cliffs, New Jersey.
Papadimitriou, C. H. (1985). “Computational complexity,” in Lawler, E. L., J. K. Lenstra, A. H.G. Rinnooy Kan, and D. B. Shmoys, eds., The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. Wiley, Chichester, UK.
Papadimitriou, C. H. (1993). Computational Complexity. Addison-Wesley, Redwood City, California.
Papadimitriou, C. H. and Steiglitz, K. (1982). Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall, Englewood Cliffs, New Jersey.
Shmoys, D. B. and Tardos, E. (1989). “Computational complexity of combinatorial problems,” in Lovász, L., R. L. Graham, and M. Groetschel, eds., Handbook of Combinatorics. North-Holland, Amsterdam.
Sipser, M. (1997). Introduction to the Theory of Computation. PWS-Kent, Belmont, California.
Stockmeyer, L. J. (1990). “Complexity theory,” in Coffman, Jr., E. G., J. K. Lenstra, and A. H.G. Rinnooy Kan, eds., Handbooks in Operations Research and Management Science; Volume 3: Computation, Chapter 8. North Holland, Amsterdam.
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
Hall, L. (2001). COMPUTATIONAL Complexity . In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_141
Download citation
DOI: https://doi.org/10.1007/1-4020-0611-X_141
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-7923-7827-3
Online ISBN: 978-1-4020-0611-1
eBook Packages: Springer Book Archive