Finding and certifying a large hidden clique in a semirandom graph

Abstract

Alon, Krivelevich, and Sudakov [Random Struct Algorithms 13(3–4) (1998), 457–466.] designed an algorithm based on spectral techniques that almost surely finds a clique of size hidden in an otherwise random graph. We show that a different algorithm, based on the Lovasz theta function, almost surely both finds the hidden clique and certifies its optimality. Our algorithm has an additional advantage of being more robust: it also works in a semirandom hidden clique model, in which an adversary can remove edges from the random portion of the graph. ©2000 John Wiley & Sons, Inc. Random Struct. Alg., 16, 195–208, 2000