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We design new polynomial-time algorithms for recovering planted cliques in the semi-random graph model introduced by Feige and Kilian. The previous best algorithms for this model succeed if the planted clique has size at least n2/3 in a graph with n vertices. Our algorithms work for planted-clique sizes approaching n1/2 — the information-theoretic threshold in the semi-random model and a conjectured computational threshold even in the easier fully-random model. This result comes close to resolving open questions by Feige and Steinhardt.
Buhai et al. (Tue,) studied this question.