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We propose a new method, probabilistic divide-and-conquer, for improving thesuccess probability in rejection sampling. For the example of integerpartitions, there is an ideal recursive scheme which improves the rejectioncost from asymptotically order $n^{3/4}$ to a constant. We show other examplesfor which a non--recursive, one--time application of probabilisticdivide-and-conquer removes a substantial fraction of the rejection samplingcost.  We also present a variation of probabilistic divide-and-conquer forgenerating i.i.d. samples that exploits features of the coupon collector'sproblem, in order to obtain a cost that is sublinear in the number of samples.

Probabilistic divide-and-conquer: a new exact simulation method, with integer partitions as an example