SONIK: Efficient In-situ All Item Rank Generation using Bit Operations

TL;DR

SONIK is a linear-time, in-situ algorithm using bit operations to efficiently compute the ranks of all input integers without explicit sorting, suitable for real-time and large data applications.

Contribution

It introduces SONIK, a novel non-comparison algorithm that computes element ranks directly at their positions using bit operations, avoiding traditional sorting overheads.

Findings

Linear time and space complexity achieved

Ranks generated in-situ without reordering

Applicable to large-scale, real-time data processing

Abstract

Sorting, a classical combinatorial process, forms the bedrock of numerous algorithms with varied applications. A related problem involves efficiently finding the corresponding ranks of all the elements - catering to rank queries, data partitioning and allocation, etc. Although, the element ranks can be subsequently obtained by initially sorting the elements, such procedures involve O(n log n) computations and might not be suitable with large input sizes for hard real-time systems or for applications with data re-ordering constraints. This paper proposes SONIK, a non-comparison linear time and space algorithm using bit operations inspired by radix sort for computing the ranks of all input integer elements, thereby providing implicit sorting. The element ranks are generated in-situ, i.e., directly at the corresponding element position without re-ordering or recourse to any other sorting mechanism.