The known algorithms run on the Pointer machine and we do not know if using a~stronger
model can help.
-For the ranking problems, the situation is completely different. We have shown
-linear-time algorithms for three important problems of this kind. The techniques,
-which we have used, seem to be applicable to other ranking problems. On the other
-hand, ranking of general restricted permutations has turned out to balance on the
-verge of $\#{\rm P}$-completeness. All our algorithms run
-on the RAM model, which seems to be the only sensible choice for problems of
-inherently arithmetic nature. While the unit-cost assumption on arithmetic operations
-is not universally accepted, our results imply that the complexity of our algorithm
-is dominated by the necessary arithmetics.
-
Aside from the concrete problems we have solved, we have also built several algorithmic
techniques of general interest: the unification procedures using pointer-based
bucket sorting (Section \ref{bucketsort}) and the vector computations on the RAM