Improved in-place associative integer sorting

A novel integer sorting technique was proposed replacing bucket sort, distribution counting sort and address calculation sort family of algorithms which requires only constant amount of additional memory. The technique was 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. In this study, the technique is improved both theoretically and practically and an algorithm is obtained which is faster than the former making it more competitive. With the improved version, n integers S[0 . . . n− 1] each in the range [0, n − 1] are sorted exactly in O(n) time while the complexity of the former technique was the recursion T (n) = T (n2 ) +O(n) yielding T (n) = O(n).