Abstract
So far we have studied efficient algorithms for a variety of problems. The time requirements for these algorithms varied from O(1) to O(log log n), O(log n), O(n), O(n log n), O(n2) and O(n3). All these algorithms are considered to be ‘good’ and are known as polynomial solutions. This is because the time requirement of each one is bounded asymptotically by a polynomial function of the size of the problem. For instance, log(n) < n for all n ⩾ 1.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliographic Notes and Further Reading
Aho, A. V., Hopcroft, J. E. and Ullman, J. D. (1974). The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Massachusetts.
Aho, A. V., Hopcroft, J. E. and Ullman, J. D. (1983). Data Structures and Algorithms, Addison-Wesley, Reading, Massachusetts.
Breuer, M. A. (1972). Design Automation of Digital Systems. Volume 1: Theory and Techniques, Prentice-Hall, Englewood Cliffs, New Jersey.
Garey, M. and Johnson, D. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco.
Hu, T. C. (1982). Combinatorial Algorithms, Addison-Wesley, Reading, Massachusetts.
Karp R. M. (1986). ‘Combinatorics, complexity and randomness’, CACM, Vol. 29, No. 2, pp. 98–110.
Kurtzberg, J. M. (1962). ‘On approximation methods for the assignment problem’, Journal of ACM, Vol. 9, No. 4, pp. 419–439.
Lin, S. (1965). ‘Computer solutions of travelling salesman problem’, Bell Sys. Tech. Journal, Vol. 44, pp. 2245–2269.
Litke, J. D. (1984). ‘An improved solution to the travelling salesman problem with thousands of nodes’, CACM, Vol. 27, No. 12, pp. 1227–1236.
Munkers, J. (1957). ‘Algorithms for the assignment and transportation problems’, Journal of SIAM. Vol. 5, pp. 32–38.
Reiter, S. and Sherman, G. (1965). ‘Discrete optimiation’, J. SIAM, Vol. 13, pp. 864–889.
Rowe, N. C. (1988). AI through PROLOG, Prentice-Hall, Englewood Cliffs, New Jersey.
Steiglitz, K. and Weiner, P. (1968). ‘Some improved algorithms for computer solutions of the TSP, Proc. 6th Annual Allerton Conference, Oct. 1968, pp. 814–821.
Author information
Authors and Affiliations
Copyright information
© 1990 Manoochehr Azmoodeh
About this chapter
Cite this chapter
Azmoodeh, M. (1990). ‘Hard’ Problems and NP-completeness. In: Abstract Data Types and Algorithms. Macmillan Computer Science Series. Palgrave, London. https://doi.org/10.1007/978-1-349-21151-7_12
Download citation
DOI: https://doi.org/10.1007/978-1-349-21151-7_12
Publisher Name: Palgrave, London
Print ISBN: 978-0-333-51210-4
Online ISBN: 978-1-349-21151-7
eBook Packages: Computer ScienceComputer Science (R0)