Interactive proofs and the hardness of approximating cliques

Authors:
Uriel Feige;Shafi Goldwasser;Laszlo Lovász;Shmuel Safra;Mario Szegedy
Affiliations:
The Weizmann Institute, Rehovot, Israel;Massachusetts Institute of Technology, Cambridge;Yale Univ., New Haven, CT;Tel-Aviv Univ., Tel-Aviv, Israel;AT&T Bell Labs. Murray Hill, NJ
Venue:
Journal of the ACM (JACM)
Year:
1996

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Abstract

The contribution of this paper is two-fold. First, a connection is established between approximating the size of the largest clique in a graph and multi-prover interactive proofs. Second, an efficient multi-prover interactive proof for NP languages is constructed, where the verifier uses very few random bits and communication bits. Last, the connection between cliques and efficient multi-prover interaction proofs, is shown to yield hardness results on the complexity of approximating the size of the largest clique in a graph.Of independent interest is our proof of correctness for the multilinearity test of functions.