  It is well known that n integers in the range [1,n^c] can be sorted in O(n)
time in the RAM model using radix sorting. More generally, integers in any
range [1,U] can be sorted in O(n sqrt{loglog n}) time. However, these
algorithms use O(n) words of extra memory. Is this necessary?
  We present a simple, stable, integer sorting algorithm for words of size
O(log n), which works in O(n) time and uses only O(1) words of extra memory on
a RAM model. This is the integer sorting case most useful in practice. We
extend this result with same bounds to the case when the keys are read-only,
which is of theoretical interest. Another interesting question is the case of
arbitrary c. Here we present a black-box transformation from any RAM sorting
algorithm to a sorting algorithm which uses only O(1) extra space and has the
same running time. This settles the complexity of in-place sorting in terms of
the complexity of sorting.
