Generalized Leapfrogging Samplesort: A Class of $O(n \log^2 n)$ Worst-Case Complexity and $O(n \log n)$ Average-Case Complexity Sorting Algorithms

TL;DR

This paper introduces a generalized class of Leapfrogging Samplesort algorithms that achieve an $O(n \, \log^2 n)$ worst-case and $O(n \, \log n)$ average-case complexity, enhancing sorting efficiency.

Contribution

It generalizes Leapfrogging Samplesort with a new parameterization, providing practical implementation and complexity analysis for improved sorting performance.

Findings

Worst-case complexity is $O(n \log^2 n)$.

Average-case complexity is $O(n \log n)$.

Practical implementation demonstrates the theoretical bounds.

Abstract

The original Leapfrogging Samplesort operates on a sorted sample of size $s$ and an unsorted part of size $s+1$. We generalize this to a sorted sample of size $s$ and an unsorted part of size $(2^k-1)(s+1)$, where $k = O(1)$. We present a practical implementation of this class of algorithms and we show that the worst-case complexity is $O(n \log^2 n)$ and the average-case complexity is $O(n \log n)$. Keywords: Samplesort, Quicksort, Leapfrogging Samplesort, sorting, analysis of algorithms.