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Proof verification and hardness of approximation problems

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5 Author(s)
Arora, S. ; Div. of Comput. Sci., California Univ., Berkeley, CA, USA ; Lund, C. ; Motwani, R. ; Sudan, M.
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The class PCP(f(n),g(n)) consists of all languages L for which there exists a polynomial-time probabilistic oracle machine that used O(f(n)) random bits, queries O(g(n)) bits of its oracle and behaves as follows: If x∈L then there exists an oracle y such that the machine accepts for all random choices but if x∉L then for every oracle y the machine rejects with high probability. Arora and Safra (1992) characterized NP as PCP(log n, (loglogn)O(1)). The authors improve on their result by showing that NP=PCP(logn, 1). The result has the following consequences: (1) MAXSNP-hard problems (e.g. metric TSP, MAX-SAT, MAX-CUT) do not have polynomial time approximation schemes unless P=NP; and (2) for some ε>0 the size of the maximal clique in a graph cannot be approximated within a factor of nε unless P=NP

Published in:

Foundations of Computer Science, 1992. Proceedings., 33rd Annual Symposium on

Date of Conference:

24-27 Oct 1992