The technique of in-place associative sorting

TL;DR

This paper introduces a novel in-place integer sorting algorithm inspired by cognitive memory stages, achieving linear time complexity with minimal extra space, and extends it to rank-sorting, outperforming traditional sorting methods.

Contribution

The paper presents a new in-place integer sorting technique based on cognitive neuroscience principles, improving time complexity and adapting it for rank-sorting.

Findings

Achieves linear time sorting with constant extra space.

Outperforms bucket sort, counting sort, and address calculation sort.

Effective for both value-sorting and rank-sorting.

Abstract

In the first place, a novel, yet straightforward in-place integer value-sorting algorithm is presented. It sorts in linear time using constant amount of additional memory for storing counters and indices beside the input array. The technique is inspired from the principal idea behind 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: (i) practicing, (ii) storage and (iii) retrieval. It is further improved in terms of time complexity as well as specialized for distinct integers, though still improper for rank-sorting. Afterwards, another novel, yet straightforward technique is introduced which makes this efficient value-sorting technique proper for rank-sorting. Hence, given an array of n elements each have an integer key, the technique sorts the elements according to their integer keys in linear time using only constant amount of additional memory. The devised technique is very practical and efficient outperforming bucket sort, distribution counting sort and address calculation sort family of algorithms making it attractive in almost every case even when space is not a critical resource.