Proof verification and hardness of approximation problems

Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, Mario Szegedy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

455 Scopus citations

Abstract

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 in L then there exists an oracle y such that the machine accepts for all random choices but if x not in L then for every oracle y the machine rejects with high probability. Arora and Safra (1992) characterized NP as PCP(log n, (loglogn)/sup 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 epsilon >0 the size of the maximal clique in a graph cannot be approximated within a factor of n/sup epsilon / unless P=NP.

Original languageEnglish (US)
Title of host publicationProceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992
PublisherIEEE Computer Society
Pages14-23
Number of pages10
ISBN (Electronic)0818629002
DOIs
StatePublished - 1992
Externally publishedYes
Event33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 - Pittsburgh, United States
Duration: Oct 24 1992Oct 27 1992

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume1992-October
ISSN (Print)0272-5428

Conference

Conference33rd Annual Symposium on Foundations of Computer Science, FOCS 1992
Country/TerritoryUnited States
CityPittsburgh
Period10/24/9210/27/92

All Science Journal Classification (ASJC) codes

  • General Computer Science

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