Approximation of coNP sets by NP-complete sets
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It is said that a set L1 in a class C1approximates a set L2 in a class C2 if L1 is a subset of L2. Approximation L1 is said to be optimal if there is no approximation L′1 such that L′1 ⊃ L1 and L′1 - L1 is infinite. When C1=P and C2=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 C1=the class of NP-complete sets and C2=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.
KeywordsPolynomial Time Optimal Approximation Single Vertex Combinatorial Algorithm Discrete Apply Mathematic
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