Approximation of coNP sets by NP-complete sets

  • Kazuo Iwama
  • Shuichi Miyazaki
Session 1A: Complexity Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 959)


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 L1 such that L1L1 and L1 - 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.


Polynomial Time Optimal Approximation Single Vertex Combinatorial Algorithm Discrete Apply Mathematic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Kazuo Iwama
    • 1
  • Shuichi Miyazaki
    • 1
  1. 1.Department of Computer Science and Communication EngineeringKyushu UniversityFukuokaJapan

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