Journal of Computer Science and Technology

, Volume 11, Issue 2, pp 126–132 | Cite as

Some undecidable problems on approximability of NP optimization problems

  • Huang Xiong 


In this paper some undecidable problems on approximability of NP optimization problems are investigated. In particular, the following problems are all undecidable: (1) Given an NP optimization problem, is it approximable in polynomial time? (2) For any polynomial-time computable functionr(n), given a polynomial time approximable NP optimization problem, has it a polynomial-time approximation algorithm with approximation performance ratior(n) (r(n)-approximable)? (3) For any polynomial-time computable functionsr(n), r'(n), wherer'(n) <r(n) a.e., given anr(n)-approximable NP optimization problem, is itr'(n)-approximable?


Computational complexity NP optimization approximability undecidability 


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Copyright information

© Science Press, Beijing China and Allerton Press Inc. 1996

Authors and Affiliations

  • Huang Xiong 
    • 1
  1. 1.Department of Computer Science and TechnologyPeking UniversityBeijing

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