Non-Deterministic Polynomial Optimization Problems and Their Approximation

  • A. Paz
  • S. Moran
Part of the International Centre for Mechanical Sciences book series (CISM, volume 266)


NP-problems are considered in this paper as recognition problems over some alphabet Σ, i.e. A ⊂ Σ* is is an NP problem if there exists a NDTM (non-deterministic Turing machine) recognizing A in polynomial time. It is easy to show that the following theorem holds true.


Polynomial Time Turing Machine STEINER Tree Node Cover Clique Cover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [AHU 74]
    A.V. AHO, J.E.HOPCROFT and J.D.ULLMAN: The Design and Analysis of Computer Algorithms, Addison Wesley (1974).Google Scholar
  2. [Co 71]
    S.A.COOK: The Complexity of Theorem Proving Procedures,3-rd STOC (1971), pp. 151–158.Google Scholar
  3. [FHK 76]
    G.N.FREDERICKSON, M.S.HECHT and C.E.KIM: Approximation Algorithms for some Routing Problems, 17-th Annual Symposium on Foundations of Computing Sciences, pp. 216–227.Google Scholar
  4. [GHS 74]
    M.R.GAREY, D.S.JOHNSON and L.STOCKMEYER: Some Simplified NP-Complete Problems,6-th STOC (1974), pp. 47–63.Google Scholar
  5. [HB 76]
    J.HARTMANIS and L.BERMAN: On Isomorphism and Density of NP and Other Complete Sets, 8-th STOC (1976), pp. 30–40Google Scholar
  6. [Jo 73]
    D.S.JOHNSON: Approximation Algorithms for Comcinatorial Problems, 5-th STOC (1973), pp.3849.Google Scholar
  7. [Ka 72]
    R.M.KARP: Reducibility among Combinatorial Problems, R.E.Miller and J.W.Thatcher (eds.), Plenum Press, N.Y. (1972), pp. 85–104.Google Scholar
  8. [Kn 74]
    D.E.KNUTH: Postcript about NP Hard Problems, SIGAT News, 23, (April 1974) pp. 15–16.Google Scholar
  9. [PS 76]
    C.H.PAPADIMITRIOU and K.STEIGLITZ: Some Complexity. Results for the TSP, 8-th STOC (1976), pp. 1–9.Google Scholar
  10. [Sa 76]
    S.SAHNI: General Techniques for Combinatorial Approximation, TR. 76–6, University of Minnesota, Dept. of Computer Sciences, (1976).Google Scholar

Copyright information

© Springer-Verlag Wien 1981

Authors and Affiliations

  • A. Paz
    • 1
  • S. Moran
    • 2
  1. 1.Dept. of Computer ScienceTECHNION-Israel Institute of TechnologyIsrael
  2. 2.Dept. of MathematicsTECHNION-Israel Institute of TechnologyIsrael

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