A Nearly Tight Sum-of-Squares Lower Bound for the Planted Clique Problem

2016 IEEE 57TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS), pp. 428-437, 2016.

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Abstract:

We prove that with high probability over the choice of a random graph G from the Erdos-Renyi distribution G(n, 1/2), the n(O(d))-time degree d Sum-of-Squares semidefinite programming relaxation for the clique problem will give a value of at least n(1/2-c(d/log n) 1/2) for some constant c > 0. This yields a nearly tight n(1/2-o(1)) bound o...More

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