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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

3 votes

Randomized algorithm?

You can certainly construct a data structure such as a hash table, which maps values from $[n^2]$ to indexes in $S$. This will enable a constant-time look-up. If you are not allowed a pre-computed da …
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