New Sorting Algorithm Wave Sort (W-Sort)
Jia Xu Wei

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 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 , average comparison complexity close to , and worst-case comparison complexity bounded by with a small constant factor, which could…
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Taxonomy
TopicsBlind Source Separation Techniques
