Feb. 9, 2024, 5:44 a.m. | Jay Mardia Kabir Aladin Verchand Alexander S. Wein

stat.ML updates on arXiv.org arxiv.org

We consider the problem of detecting a planted clique of size $k$ in a random graph on $n$ vertices. When the size of the clique exceeds $\Theta(\sqrt{n})$, polynomial-time algorithms for detection proliferate. We study faster -- namely, sublinear time -- algorithms in the high-signal regime when $k = \Theta(n^{1/2 + \delta})$, for some $\delta > 0$. To this end, we consider algorithms that non-adaptively query a subset $M$ of entries of the adjacency matrix and then compute a low-degree polynomial …

algorithms cs.cc cs.ds detection faster graph low polynomial random signal stat.ml study transitions

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