Consider an array of N elements. M elements, and M positions in the array, are marked. You want to permute the array so that the M marked elements end up in the M marked positions. What is the name of the problem?
Note that solving this problem in time O(N) is trivial in the "standard" RAM model, but it is not if one adds additional complications such as parallelism or errors. For example, a routing network that solves the problem is called a (self-routing) superconcentrator, and building one with O(N) elements took significant effort.