Abstract
A large class of NP optimization problems called MNP are studied. It is shown that Rmax(2) is in this class and some problems which are not likely in Rmax(2) are in this class. A new kind of reductions, SL-reductions, is defined to preserve approximability and nonapproximability, so it is a more general version of L-reductions and A-reductions. Then some complete problems of this class under SL-reductions are shown and it is proved that the max-clique problem is one of them. So all complete problems in this class are as difficult to approximate as the max-clique problem.
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This work is supported under The National Natural Science Foundation of China grant No. 69373006 and The National Hi-Tech Programme of China grant No. 863-306-05-03-04. The extended abstract of this paper was accepted by COCOON’95 and appeared in LNCS 959[1].
Cheng Qi received his B.S. degree in computer software from Nankai University and his M.S. degree in computer science from Fudan University. He is currently an Assistant Professor in the Department of Computer Science at Fudan University. His areas of interest are random algorithm and combinatorics.
Zhu Hong is a Professor in the Department of Computer Science at Fudan University. His current interests are computational complexity, combinatorics and cryptography.
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Cheng, Q., Zhu, H. MNP: A class of NP optimization problems. J. of Comput. Sci. & Technol. 12, 306–313 (1997). https://doi.org/10.1007/BF02943150
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DOI: https://doi.org/10.1007/BF02943150