Complexity of Exact and Approximate Solution of Problems. An Introduction

  • Giorgio Ausiello
Part of the International Centre for Mechanical Sciences book series (CISM, volume 284)


NP-complete optimization problems are frequently encountered in the optimal design of computer systems,operating systems, databases etc. In this paper a discussion of the basic techniques which lead to the characterization of the complexity of optimization problems is presented. The class of optimization problems which are associated to NP-complete decision problems is then presented and various algorithmic techniques for the approximate solution of such problems are introduced. Finally necessary and sufficient conditions for the approximability of optimization problems are given.


Approximate Solution Polynomial Time Turing Machine Travel Salesman Problem Knapsack Problem 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Remarks and References

  1. Aho, A.V., J.E. Hoperoft, J.D. Ullman: The design and analysis of computer algorithms, Addison Wesley, 1974.Google Scholar
  2. Cook, S.A.: The complexity of theorem proving procedures, Proc. 3rd Ann. ACM Symp. on Theory of Coputing, 1971.Google Scholar
  3. Karp, R.M.: Reducibility among combinatorial problems, in R.E.Muller and J.W.Thatcher (eds.), Complexity of Computer computations, Plenum Press, 1972.Google Scholar
  4. M.R. Garey and D.S. Johnson: Computers and intractability. A guide to NP-completeness, Freeman, 1979.Google Scholar
  5. Horowitz, E., S. Sahni: Fundamentals of computer algorithms, Computer Science Press, 1978.Google Scholar
  6. Papadimitrou, C.H. and K. Steiglitz: Combinatorial optimization: Algorithms and complexity, Prentice Hall, 1982.Google Scholar
  7. Paz, A. and S. Moran: NP-optimization problems and their approximation, Proc 4th Int. Symposium on Automatic, Languages and Programming, LNCS, Springer Verlag, 1977.Google Scholar
  8. Ausiello, G. A. Marchetti Spaccamela, M. Protasi: Toward a unified approach for the classification of NP-complete optimization problems, Theoretical Computer Science, 12, 1980.Google Scholar
  9. Ausiello, G., A. Marchetti Spaccamela and M. Protasi: Full approximability of a class of problems over power sets, 6th Colloquium on Trees in Algebra and Programming, LNCS, Springer Verlag, 1981.Google Scholar
  10. Korte, B. and R. Schrader: On the existence of fast approximation schemes, Report No. 80163 Institut für Ökonom. und Op. Res.; REWU, 1980.Google Scholar

Copyright information

© Springer-Verlag Wien 1984

Authors and Affiliations

  • Giorgio Ausiello
    • 1
  1. 1.Dipartimento di Informatica e SistemisticaUniversità di Roma “La Sapienza”Italy

Personalised recommendations