Before revision:  We present space-efficient algorithms for sorting, dense ranking and (competitive) ranking S on the word RAM model with word size \Omega(\log N)  . Our algorithms run in O(k + N{\log N}) time and use O(N) bits.
After revision:  We present space-efficient algorithms for sorting, dense ranking and (competitive) ranking S on the word RAM model with word size \Omega(\log N) bits . Our algorithms run in O(k + N{\log N}) time and use O(N) bits.