  In this paper, we introduce polynomial time algorithms that generate random
3-noncrossing partitions and 2-regular, 3-noncrossing partitions with uniform
probability. A 3-noncrossing partition does not contain any three mutually
crossing arcs in its canonical representation and is 2-regular if the latter
does not contain arcs of the form $(i,i+1)$. Using a bijection of Chen {\it et
al.} \cite{Chen,Reidys:08tan}, we interpret 3-noncrossing partitions and
2-regular, 3-noncrossing partitions as restricted generalized vacillating
tableaux. Furthermore, we interpret the tableaux as sampling paths of
Markov-processes over shapes and derive their transition probabilities.
