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Sampling without replacement with unequal probabilities - is linear runtime possible?

In search of faster weighted sampling without replacement , the following question arose:

Is there an algorithm that implements random sampling without replacement with unequal selection probabilities using linear time at the input size? An O (n log n) implementation was proposed in response to this question - can this be improved?

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language-agnostic algorithm random-sample
Feb 27 '13 at 14:44
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