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Low-degree phase transitions for detecting a planted clique in sublinear time
Using (a bound on) the conditional low-degree likelihood ratio as a potential function, we show that for every non-adaptive query pattern, there is a highly structured query pattern of the same size that is at least as effective.
Logspace Reducibility From Secret Leakage Planted Clique
Known reductions to these problems are all randomized and need polynomially many random bits to implement.
Is the space complexity of planted clique recovery the same as that of detection?
We show that for k=Omega(sqrt{n}), the recovery problem can be solved in O((log*{n}-log*{k/sqrt{n}}) log n) bits of space.
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