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

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