Some undecidable problems on approximability of NP optimization problems
- 28 Downloads
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?
KeywordsComputational complexity NP optimization approximability undecidability
Unable to display preview. Download preview PDF.
- Hopcroft J E, Ullman J D. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley Publishing Company, 1979.Google Scholar
- 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.Google Scholar