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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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