Skip to main content

‘Hard’ Problems and NP-completeness

  • Chapter
Abstract Data Types and Algorithms

Part of the book series: Macmillan Computer Science Series

  • 69 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

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.

    Google Scholar 

  • Aho, A. V., Hopcroft, J. E. and Ullman, J. D. (1983). Data Structures and Algorithms, Addison-Wesley, Reading, Massachusetts.

    Google Scholar 

  • Breuer, M. A. (1972). Design Automation of Digital Systems. Volume 1: Theory and Techniques, Prentice-Hall, Englewood Cliffs, New Jersey.

    Google Scholar 

  • Garey, M. and Johnson, D. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco.

    Google Scholar 

  • Hu, T. C. (1982). Combinatorial Algorithms, Addison-Wesley, Reading, Massachusetts.

    Google Scholar 

  • Karp R. M. (1986). ‘Combinatorics, complexity and randomness’, CACM, Vol. 29, No. 2, pp. 98–110.

    Article  Google Scholar 

  • Kurtzberg, J. M. (1962). ‘On approximation methods for the assignment problem’, Journal of ACM, Vol. 9, No. 4, pp. 419–439.

    Article  Google Scholar 

  • Lin, S. (1965). ‘Computer solutions of travelling salesman problem’, Bell Sys. Tech. Journal, Vol. 44, pp. 2245–2269.

    Article  Google Scholar 

  • Litke, J. D. (1984). ‘An improved solution to the travelling salesman problem with thousands of nodes’, CACM, Vol. 27, No. 12, pp. 1227–1236.

    Article  Google Scholar 

  • Munkers, J. (1957). ‘Algorithms for the assignment and transportation problems’, Journal of SIAM. Vol. 5, pp. 32–38.

    Google Scholar 

  • Reiter, S. and Sherman, G. (1965). ‘Discrete optimiation’, J. SIAM, Vol. 13, pp. 864–889.

    Google Scholar 

  • Rowe, N. C. (1988). AI through PROLOG, Prentice-Hall, Englewood Cliffs, New Jersey.

    Google Scholar 

  • 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.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

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)

Publish with us

Policies and ethics