The planted clique conjecture states that no polynomial-time algorithm can find a hidden clique of size $k \ll \sqrt{n}$ in an $n$-vertex Erd\H{o}s--R\'enyi random graph with a $k$-clique planted. In this paper, we prove the equivalence among many (in fact, \emph{most}) variants of planted clique conjectures, such as search ... more >>>

We give an algorithm for finding an $\epsilon$-fixed point of a contraction map $f:[0,1]^k\rightarrow [0,1]^k$ under the $\ell_\infty$-norm with query complexity $O (k^2\log (1/\epsilon ) )$.

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We consider the task of locally correcting, and locally list-correcting, multivariate linear functions over the domain $\{0,1\}^n$ over arbitrary fields and more generally Abelian groups. Such functions form error-correcting codes of relative distance $1/2$ and we give local-correction algorithms correcting up to nearly $1/4$-fraction errors making $\widetilde{\mathcal{O}}(\log n)$ queries. This ... more >>>