New Sorting Algorithm Wave Sort (W-Sort)

TL;DR

Wave Sort is a new in-place sorting algorithm that offers consistent performance, fewer comparisons than quicksort, and guarantees logarithmic recursion depth through dynamic pivot selection.

Contribution

It introduces Wave Sort, a novel in-place sorting method with a dynamic pivot strategy that improves consistency and efficiency over existing comparison sorts.

Findings

Requires approximately 24% fewer comparisons than quicksort on average.

Performs close to the theoretical minimum comparison count.

Guarantees logarithmic recursion depth and robust pivot selection.

Abstract

Modern comparison sorts like quicksort suffer from performance inconsistencies due to suboptimal pivot selection, leading to $(O(N^2))$ worst-case complexity, while in-place merge sort variants face challenges with data movement overhead. We introduce Wave Sort, a novel in-place sorting algorithm that addresses these limitations through a dynamic pivot selection strategy. Wave Sort iteratively expands a sorted region and selects pivots from this growing sorted portion to partition adjacent unsorted data. This approach ensures robust pivot selection irrespective of dataset size, guarantees a logarithmic recursion stack depth, and enables efficient in-place sorting. Our analysis shows a best comparison complexity of $(N-1)$, average comparison complexity close to $(\log_2(N)!)$, and worst-case comparison complexity bounded by $(O(N(\log(N))^2))$ with a small constant factor, which could be reduced to $(O(N\log(N)))$ with hybrid sorting. The algorithm can be easily expanded to be hybridized with other sorting algorithms. Experimental results demonstrate that Wave Sort requires significantly fewer comparisons than quicksort on average (approximately 24% less) and performs close to the theoretical minimum $(\log_2(N)!)$. Wave Sort offers a compelling alternative for applications demanding consistent, predictable, and in-place sorting performance.