Those are very interesting algorithms, which I was not familiar with. Thank you very much for implementing them.
However, no offense to Mr. Knuth or his S algorithm, but selecting n unique elements from an array containing N elements only needs to consider n elements. The solution below is based on a linear shuffle algorithm I saw on perlmonks. Instead of shuffling all N elements of the array, I instead shuffle the first n elements and return only those shuffled.
The basic operation of the linear shuffle is: For each element in the array, randomly choose any element from this element up to the end of the array, and swap the two elements. Please see the original linear shuffle code for a clear demonstration of how to shuffle an entire array.
In the code above, I use a shadow hash %i to store the indices of the shuffled elements of $array. I do this so I can choose a random set from $array without changing the contents of $array, and without copying the entire array. I use a hash %i and defined() tests instead of having to initialize an entire array @i with (0..@$array-1).
I'm not sure of the original requirements of the algorithm, but even using a shadow hash instead of copying the array, my code does use more memory than Knuth's S algorithm. This may not be acceptable in all cases, but if it isn't, then you probably shouldn't be using perl :)
Depending on your requirements, it may be faster or more efficient to chop out the optimizations, which only make sense for a large $array compared to $n (and/or, if you don't want the array to actually be shuffled).
Thanks for the good and inspiring post!
Update: Ah, your point is well taken: In the context of any data storage which allows only linear access to the records, Knuth's algorithm is definitely the better solution. I'm sorry I seemed to have missed this point.
I do very much like the second algorithm you presented, probably because I didn't miss the point of that one :) I think that most of the time that would be the more appropriate algorithm for my uses when I'm dealing with file access. "Select N random lines from a file" seems like a common task which this would solve efficiently. Most of the time I'm not going to know how many lines I have in the file without counting, which defeats the purpose.