In-place associative integer sorting

Abstract: A novel integer value-sorting technique is proposed replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. It requires only constant amount of additional memory. The technique is inspired from one of the ordinal theories of "serial order in behavior" and explained by the analogy with the three main stages in the formation and retrieval of memory in cognitive neuroscience namely (i) practicing, (ii) storing and (iii) retrieval. Although not suitable for integer rank-sorting where the problem is to put an array of elements into ascending or descending order by their numeric keys, each of which is an integer, the technique seems to be efficient and applicable to rank-sorting, as well as other problems such as hashing, searching, element distinction, succinct data structures, gaining space, etc.