Abstract
It is said that a set L 1 in a class C 1 approximates a set L 2 in a class C 2 if L 1 is a subset of L 2. Approximation L 1 is said to be optimal if there is no approximation L′1 such that L′1 ⊃ L 1 and L′1 - L 1 is infinite. When C 1=P and C 2=NP, it is known that there is no optimal approximation under a quite general condition unless P=NP. In this paper we discuss the case where C 1=the class of NP-complete sets and C 2=coNP. A similar result as above that shows the difficulty of the optimal approximation is obtained. Approximating coNP sets by NP-complete sets play an important role in the efficient generation of test instances for combinatorial algorithms.
This research was supported by Scientific Research Grant, Ministry of Education, Japan, No. 04650318, and Engineering Adventure Group Linkage Program (EAGL), Japan.
Research Fellow of the Japan Society for the Promotion of Science. This research was supported by Scientific Research Grant, Ministry of Education, Japan, No. 2273
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Iwama, K., Miyazaki, S. (1995). Approximation of coNP sets by NP-complete sets. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030815
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DOI: https://doi.org/10.1007/BFb0030815
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