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Some undecidable problems on approximability of NP optimization problems

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Abstract

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?

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References

  1. Garey M R, Johnson D S. “Strong” NP-complete results: Motivation, examples, and implications.JACM, 1978, 25: 499–508.

    Article  MATH  MathSciNet  Google Scholar 

  2. Hopcroft J E, Ullman J D. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley Publishing Company, 1979.

  3. Kolaitis P G, Thakur M N. Approximation properties of NP minimization classes. InProc. 6th Annual Conf. on Structure in Complexity Theory, 1991, pp.353–366.

  4. Papadimitriou C H, Yannakakis M. Optimization, approximation, and complexity classes.Journal of Computer and System Science, 1991, 43: 425–440.

    Article  MATH  MathSciNet  Google Scholar 

  5. Paz A, Moran S. Non-deterministic polynomial optimization problems and their approximation.Theoretical Computer Science, 1981, 15: 251–277.

    Article  MATH  MathSciNet  Google Scholar 

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Author notes

  1. Huang Xiong

    Present address: Beijing University of Aeronautics & Astronautics, Box 2-52, 100083, Beijing

Authors and Affiliations

  1. Department of Computer Science and Technology, Peking University, 100871, Beijing

    Huang Xiong

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  1. Huang Xiong
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Additional information

Research supported in part by the National High-Tech Programme of China.

Huang Xiong received his B.S. and M.S. degrees in computer science from Peking University in 1992 and 1995 resp. Now he is a Ph.D. candidate in Beijing University of Aeronautics & Astronautics. His major research interests are in complexity theory, design and analysis of algorithms.

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Huang, X. Some undecidable problems on approximability of NP optimization problems. J. of Comput. Sci. & Technol. 11, 126–132 (1996). https://doi.org/10.1007/BF02943528

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  • DOI: https://doi.org/10.1007/BF02943528

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