Sampling without replacement with unequal probabilites — linear run time possible?

问题

In search for a faster weighted sampling without replacement, the following question came up:

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

来源：https://stackoverflow.com/questions/15114898/sampling-without-replacement-with-unequal-probabilites-linear-run-time-possib