Binar Sort: A Linear Generalized Sorting Algorithm

TL;DR

Binar Sort introduces a new linear sorting algorithm that leverages a universal property of data other than order, challenging the traditional linearithmic lower bound of comparison-based sorting algorithms.

Contribution

The paper presents Binar Sort, a novel linear sorting algorithm that exploits an alternative universal data property, expanding the scope of efficient sorting methods beyond comparison-based approaches.

Findings

Binar Sort achieves linear time complexity.

It utilizes a different universal property of data for sorting.

The algorithm broadens the theoretical understanding of sorting possibilities.

Abstract

Sorting is a common and ubiquitous activity for computers. It is not surprising that there exist a plethora of sorting algorithms. For all the sorting algorithms, it is an accepted performance limit that sorting algorithms are linearithmic or O(N lg N). The linearithmic lower bound in performance stems from the fact that the sorting algorithms use the ordering property of the data. The sorting algorithm uses comparison by the ordering property to arrange the data elements from an initial permutation into a sorted permutation. Linear O(N) sorting algorithms exist, but use a priori knowledge of the data to use a specific property of the data and thus have greater performance. In contrast, the linearithmic sorting algorithms are generalized by using a universal property of data-comparison, but have a linearithmic performance lower bound. The trade-off in sorting algorithms is generality for performance by the chosen property used to sort the data elements. A general-purpose, linear sorting algorithm in the context of the trade-off of performance for generality at first consideration seems implausible. But, there is an implicit assumption that only the ordering property is universal. But, as will be discussed and examined, it is not the only universal property for data elements. The binar sort is a general-purpose sorting algorithm that uses this other universal property to sort linearly.